J
Bmwchonm.
1977.
Vol.
IO.
pp.
141-162
Pergamon Press. Printed I” GreatBritain
THE MECHANICAL BEHAVIOUR OF INTRACONDYLAR CANCELLOUS BONE OF THE FEMUR AT DIFFERENT LOADING RATES* PAUL DUCHEYNE$, Luc HEYMAN$ MARC MARTENS, ETIENNEAERNOUDT. PAUL DE MEESTERand
JOZEFC. MULIER
Katholieke Universiteit te Leuven, Department of Metallurgy, B-3030 Heveriee and University Hospitals, B-3041 Pellenberg. Belgium Abstract-The compressive properties of human cancellous bone of the distal intracondylar femur in its wet condition were determined. Specimens were obtained from six cadaveric femora and were tested at a strain rate of 0.002, 0.10 and 9.16 see- i. It was found that the compressive strength decreases with an increasing vertical distance from the joint. The highest compressive strength level was recorded in the posterior medial condyle. Correlations among the mechanical properties, the bulk specimen density and the bone mineral content yield (i) highly significant correlations between the compressive strength and the elastic modulus (ii) highly significant correlations between the compressive strength or the modulus of elasticity and the bulk specimen density (iii) a doubtful correlation between the compressive strength and the bone mineral content. All recorded graphs of the impact loaded specimens displayed several well defined stress peaks, unlike the graphs recorded at low loading rates. It can be concluded that upon impact loading the localized trabecular failure which is associated with each peak, does not affect the spongy bone’s stress capacity in a detrimental way.
INTRODUCTION
Mechanical properties of bone have been studied intensively. Most research efforts have been devoted to the determination of the mechanical behaviour and characteristics of compact cortical bone. Some recent literature surveys account for the gathered knowledge
of the mechanical behaviour of cortical bone (Currey, 1970; Evans 1973; Reilly and Burstein 1974). The weight bearing bones of the human skeleton consist of an outer shell of compact cortical bone and an inner spongy structure of cancellous bone. The knowledge of the mechanical properties of the latter type can be considered as important for several reasons. Firstly, the cancellous bone is an integrated part of the bone as an anatomical structure. In order to describe the mechanical functioning of a bone, the mechanical properties of all its components including the cancelbus bone should be known. A recent example which pertains to this point is given by the work of Hayes, Swenson and Schurmann (1976) which suggests that the incidence and nature of tibia1 plateau fractures are influenced by the mechanical characteristics of the subchondral bone. Secondly, the knowledge of the mechanical properties of cancellous bone enhances the fundamental understanding of how cancellous bone behaves upon loading and clarifies the relationship among mechanical properties, mechanical behaviour and trabecular structure. Thirdly, since total joint replacement prostheses are mainly in contact with trabecular bone, improve* Received 23 February 1917. Present address: (Sept. 1976Aug.
t
1977) Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611, U.S.A. 747
ments of the functioning and the design of present prostheses rely upon the exact and accurate knowledge of cancellous bone properties. The current development of new prosthetic devices with bone ingrowth at the interface demands for a good understanding of the trabecular bone properties. The compressive strength properties of cancellous bone which have been determined most frequently are those of human vertebral spongy bone. These data were summarized by Evans (1973). However, with respect to prosthetic total joint replacements the knowledge of the mechanical behaviour of the cancellous bone of long bones should be readily availabie. Directional differences of the compressive strength and the modulus of elasticity for different trabecular regions of a human femur were reported by Knese (1958). Behrens, Walker and Shoji (1974) studied the cancellous bone of several normal and arthritic knees. Parameters which were included in their study were the orientation and position of the specimens, the bulk specimen density, the linear absorption coefficient and the bone material density. Schoenfeld, Lautenschlager and Meyer (1974) determined the ultimate compressive strength and the stress relaxation of human cancellous bone from the femoral head. Their specimens were obtained from femoral heads removed at surgery for total hip joint replacement. From their report it is not clear whether the cancellous bone was healthy. Pugh, Rose and Radin (1973a and b) studied the elastic and viscoelastic properties of human subchondral cancellous bone of the femoral condyles and established a relationship between mechanical properties and trabecular structure. The present paper deals with the compressive properties of human cancellous bone of the distal in-
748
PAUL DUCHEYNE et a[.
tracondylar femur. The compressive strength and the elastic modulus of cylindrical hone samples were determined by compressive tests at both low and impact loading rates. Since bones are subjected in uiuo to a high loading rate, it is essential to test spongy bone samples at a high loading rate to obtain valuable data on the compressive strength and elastic modulus of cancellous bone. Tests at low loading rates were also included in this study in order to compare the mechanical behaviour of cancellous bone at a physiological loading rate with the behaviour at rates commonly used by others (Galante, Rostoker and Ray, 1970; Schoenfeld, Lautenschlager and Meyer, 1974; Behrens, Walker and Shoji, 1974). Correlations among the mechanical properties and the bulk specimen density, the position, the bone mineral content and the trabecular structure were attempted. METHODS
Sawing of the blocks into slabs
I lMilling of the,slab surfacesl
I
Drilling of cylindrical bone SaDhS
I
I
AND MATERIALS
A
Figure 1 details the successive steps followed during the preparation of the specimens. The study was performed on human autopsy material, which was stored in a deep freeze at - 35°C until specimen preparation. The autopsy subjects included 2 females and 4 males, ranging in age from 43 to 77 yr. Data on the age, sex and physical activity of the patients are summarized in Table 1. There was no history of bone or joint disease, which was confirmed by radiographic examination.
IDrying and defatting of
the samplcs~
Density measurements
*
Preparation of the compression specimens
The distal femoral epiphyses were embedded in foam and the position of the femurs in the surrounding foam block was determined radiographically. This technique provides reproducible slabs from the distal epiphyses, parallel with a plane tangential to the condyles. Five slabs with a thickness of about 8 mm were sawn from each femur. In order to assure parallel surfaces, the slabs were milled at -32°C. Only at this or lower freezing temperatures one can expect not to damage the trabeculae upon milling. Core drills with an inner diameter of 5 mm were used to cut cylindrical specimens. Vertically oriented specimens were obtained. The localization of the specimens was chosen to cover a range of varying radiographical density. Figure 2 shows the second slab of femur F28 before and after removal of the specimens. During preparation the specimens
Fig. 1. The subsequent steps of the specimen preparation. were kept wet constantly and preserved at -32°C between successive steps. Table 2 represents the total number of specimens per femur. Volume and density measurements
Prior to the mechanical tests, the diameter and the length of each specimen was determined using a Cambridge measuring microscope. The samples were weighed subsequently. These data allow the calculation of the wet apparent bulk density (a,), which is defined by the wet sample weight divided by the total sample volume. The compression tests
Two femurs (F31 and F74) were tested in compression on an Instron TT-DM-L testing machine at a
Table 1. Data on the obtained femurs Femur number
Age
F31 F74 F23 F28 F67 F8
63 49 47 77 65 43
Sex
M M
Physical activity information not obtained heavy work p&t office worker heavy work in the mines information not obtained housework
Femur
Loading rate (cm/min)
Strain rate W-V
left left right left right right
0.1 5 440 440 440 440
0.002 0.10 9.16 9.16 9.16 9.16
749
Fig. 2. The second slab of femur F28 before and after removal of the cylindrical specimens.
Fig. 3. The high loading rate testing device. The cancellous bone specimen can be seen on the lower fixture and is surrounded by a steel ring. The extensometu is attached to the same fixture.
Mechanical behaviour of cancellous bone Table 2. Number of specimens per femur Femur
F31
Numberofspecimens 42
F74 F23 F28 42
25
24
F67
F8
25
25
loading rate of 0.1 and 5 cm/min. The recorder chart was driven at different constant speeds to obtain a 45 degree slope during the elastic deformation. Each test was performed within two minutes of air exposure of the specimen. The samples of the other four femurs (F23, F28, F67 and F8) were tested at a high loading rate @Ocm/min) on a different, hydraulically operating testing device (see Fig. 3). The specimens were positioned on the extension of the upwards moving piston and compressed against the upper die. The bone specimens were surrounded by a steel ring, which at the end of the test stopped the upward motion of the piston by the release of the hydraulic energy into elastic deformation of the ring. These rings, ground to a precise height, made it possible to compress the specimens over a predetermined length yielding deformations in the range of 5-15%. The microscopic structure of the tested specimens could still be examined, as only limited amounts of damage were permitted. The displacement was measured with an extensometer based on the principle of magnetic inductance varying with the position of a central movable pin. The signals from the load transducer and the extensometer were recorded on an analogdigital recorder (Biomation Waveform Recorder, model 1015) and, for storage purposes, on a seven channel tape recorder (Philips, ana-log 7). Load-deIIection curves were plotted on an x-y recorder (Honeywell, model 550) using the output of the analogdigital recorder. Density measurements After compression testing the specimens were defatted ultrasonically for 2 hr in a 50% ether-5004 ethanol solution. They were allowed to dry for 24 hr at 55°C. This was followed by the determination of the dry apparent bulk density (6,) defined by the dry sample weight divided by the total sample volume. Examination of the structure In order to study the failure mechanisms and the relationship among trabecular structures, mechanical properties and apparent density, twenty eight impact loaded specimens were selected and embedded in an epoxy resin (Technovit) or in methyl methacrylate. As several peaks could appear in the loaddeformation graphs, specimens with the same density displaying curves with a different number of peaks were selected. Apart from the choice. of specimens following this main criterion, specimens were selected on the basis of some secondary criteria: the variation of the density (F28 and F8), the strain at the top of the second peak (F67) and the variation of the modulus of elasticity (F23).
751
The specimens were cut parallel with their longitudinal axis by the use of a low deformation, precision saw with a diamond blade (Buehler: Isomet). After polishing the structure was examined on a reflected light microscope (Neophot 2-Jena). Bone mineral content determination The bone mineral content of 29 samples was determined by ashing at 500°C for 48 hr and subsequent weighing. The experimental absolute error on the bone mineral content was assessed on the basis of double independent measurements of the dry specimen weight and the ash weight; the differences between the two independent measurements were considered the absolute errors on these variables; the absolute error of the bone mineral content was calculated using these absolute errors on dry specimen and ash weight.
RESULTS The compression
tests at the lower loading rates
A typical recorded graph of a compression test at a loading rate of 5 cm/min is shown in Fig. 4. Once the peak value is reached a stepwise decrease of the load is observed. The peak value is considered to be the compressive strength a; the elastic modulus E is determined by the constant slope of the initial loadtime curve. The compressive strength was correlated with the elastic modulus, the wet apparent bulk specimen density (6,) and the apparent density after drying and defatting (6,). Linear regression analyses yield the results which are summarized in Table 3. A, and A2 are the constants of the linear relation Y= A, + A2X. R is the correlation coefficient, a value close to 1 indicating a high degree of correlation. K is the number of representation points used for the particular regression and YM and XM are the mean values of the Y and X parameters. High positive correlations @ < 0.001) were noted for all relations tested. The variation of the compressive strength with the location of the cancellous bone specimens is shown in Fig. 5. The strongest region was found to be the medial posterior side. The specimens removed from the more distal slabs, proved to be stronger. It is important to notice that the fifth slab usually did not include the condyles. The compression tests at an impact loading rate A typical recorded curve of a compression test at a loading rate of 44Ocm/min is represented in Fig. 6. All recorded graphs display several well defined peaks; the top values of the peaks were considered as consecutive compressive strengths er, c2.. . . . The elastic modulus (E,, El,. . .) was determined as the constant slope of the stress-strain curves. The strain,
752
PAULDUCHEYNE et al. b
-P
7J
u 0
time
Fig. 4. A schematical load-time curve of a sample tested
at a loading rate of 5 cm/min.
The results of the linear regression analyses indicate the existence of a significant correlation between compressive strength and wet and dry apparent bulk specimen density (Fig. 7). The correlations between the elastic modulus and the wet and dry apparent density were found to vary in the same way as the correlation among compressive strength and wet and dry apparent densities. No significant correlation between the compressive strength and the strain at peak values was found. Neither could a significant correlation be established between the strain at the peak values and the apparent bulk specimen density. The strain at the different peaks could, however, be correlated with each other. The regression relating the compressive strength to the elastic modulus is highly significant: Fig. 8 @ < 0.001). Plotting the consecutive compressive strengths against each other, a highly significant correlation was obtained (p < 0.001). The equations u, = o2 and o1 = o3 lie within the 99% confidence limit of the established correlations, except for values of u1 lower than 0.50 kg/mm2 in the correlation between g1 and u2: Fig. 9.
corresponding with the peak values was also calculated (PI, Pt, . . . .). Similar to the spongy bone specimens tested at the lower loading rates, the testing at high loading rates revealed a wide variation of the tist compressive strength with regard to the specimen’s location. The relation between location and compressive strength shows the same apparent tendencies for all loading rates used. ‘Most spongy bone specimens have a compressive strength in the range of 0.10-2.30 kg/mm2 and the value of the elastic modulus is mainly between 6 and 300 kg/mm*. As an example, the results of F23 are listed in Table 4. The highest recorded values of the compressive strength for all femurs are represented in Table 5. The compression stresses associated with the different peaks (gal, Q~,. . . .) were correlated with their elastic modulus (E,, El,. . . .) and strain at the peak value. Correlations with the apparent wet (8,) and dry (c&-j bulk specimen density were attempted as well. The experimental results were correlated for each femur separately and for the four femurs together. The correlations covering data points of all 4 femurs, are called the global correlations. As an example the results of the linear regression analyses of F23 are presented in Table 6. The correlation coefficient and the number of representation points of the global analyses are compiled in Table 7. The relations between the compressive strength, and .the apparent bulk densities are plotted on Fig. 7, the relation between the elastic modulus and the compressive strength in Fig. 8 and the relation between first and second com- Fig. 5. The variation of the compressive strength (expressed in kg/mm’) with the position (F74). pressive strength in Fig. 9. Table 3. Results of the linear regression analysis for the specimens tested at the lower loading rates. The compressive strength and the elastic modulus are expressed in kg/mm* Y
F31 (0.1cm/min)
A2
X
R
K
XM
YM
d
0.01 2.102 2.232
E
- 2.05 -0.378
6. s,
0.78 0.80 0.88
36 42 42
38.02 1.22 0.41
0.61 0.56 0.56
u u u
- 0.022 - 1.85 -0.33
0.03 1.993 1.974
0.84 0.87 0.83
36 38 38
15.09 1.08 0.34
0.36 0.36 0.36
u a
F74 (5 cm/min)
Al 0.216
Mechanical behaviour of cancellous bone
2.69
I
nw 1
6.99
1
strain
[%I
Fig. 6. The stress-strain curve of a specimen tested at a loading rate of 440cm/min.
reaction force reaches a peak at heel strike and toeoff. At that moment the angle between the joint reaction force and the femoral axis is approx. 20”. Behrens, Walker. and Shoji (1974) who have studied the variation of the compressive strength of intracondylar cancellous bone with a variation in angular position with regard to the femoral axis, have suggested that the highest compressive strength would have been recorded with specimens oriented under an angle of 20” with the femoral axis. Since the orientation of our tested compression specimens approaches the orientation of the peak force at walking and presumably the orientation of maximum strength, differences in strength due to varying location can be interpreted on the basis of the actual functioning of the intracondylar trabecular bone. No statistical analysis on the relation between location and compressive strength was performed. Due to differences in physical activity, the compressive strength at functionally equivalent locations of femurs of different individuals can vary by a factor 2 to 3. This variation is superposed on the variation with the location within each femur. Furthermore, it is very uncertain whether bone specimens were obtained DlSClJS!SlON in identical functional locations. Comparing the The irzfluence of the location strength within each femur location by location and The compressive strengths measured in this study observing identical trends within each femur is more meaningful than comparing the mean value of all yield a map of the strength of intracondylar cancellous bone of the femur at an orientation parallel to femurs for each location. As a matter of fact the stanthe vertical joint reaction force at stance phase. This dard deviation on the mean compressive strength is direction is not the one at which the highest peak so large due to differences between individuals that the statistical analysis performed in this way would loads are reached during activities such as walking and climbing and descending stairs. It is however reject a significant variation with location. From the results it follows that the compressive close to the direction of the peak forces during the most frequent daily activity with a considerable resul- strength decreases with increasing vertical distance to tant loading, which is walking. In fact, the results of the joint. This is not surprising since the main ~~~ mechanical function of the trabecular bone is the disMorrison (1968) indicate that durinn walkine the ioint .
The microscopic examination of sections parallel to the compression direction revealed some striking variations of trabecular patterns. The weaker specimens were composed of columnar arrangements of trabeculae; the stronger samples displayed a branched trabecular structure. Comparing specimens with the same density but a different compressive strength, it was found that the stronger specimens had thicker and more branched trabeculae. Any sample which was tested beyond its first compressive strength showed structural damage of the trabeculae. Trabeculae failed by transverse splitting (Fig. 1Oa)or by shearing (Fig. lob) of their lamellae. The bone mineral content, determined by ashing varied between 62 and 70%. The absolute error on the bone mineral content was assessed to be 0.33% at the mean, with S.D. of 0.21%. When plotting the bone mineral content against the compressive strength ui a poor correlation was obtained. The level of significance was p < 0.1 and the correlation coefficient 0.28. Figure 11 shows the large scatter of representation points of this relation.
I
2’: 2Y 22 3B 3D 4A 4B 4D 4E SB SC
1C IE IZ
Specimen number
1.12 1.33 0.69 0.91 0.07 0.37 0.45 0.35 0.60 0.14 0.40 0.87 0.07
0.60
I.41
169.4 23.3 88.6 152.8 39.8 13.5 1.9 19.0 22.7 17.3 31.2 5.3 19.8 67.8 4.8
1.99 6.22 3.13 2.57 3.12 2.59 8.18 4.60 3.51 3.91 3.64 4.07 3.50 2.26 2.27 1.43 1.07 1.45 0.78 1.07 0.11 0.37 0.69 0.24 0.76 0.04 0.37 0.75 0.07 z 97:6 32.2 72.9 4.2 29.7 29.2 10.4 16.9 2.6 9.2 79.8 3.8
105.9
4.13 5.68 4.87 7.96 6.99 12.70 9.81 7.47 9.18 6.48 15.04 7.44 6.51 5.55 0.27 0.79 0.06
0.87
-
-
12.64 13.81 11.43 15.33 12.65 13.11 10.96 IO.10
69.7 14.7 18.6 35.1 23.3 28.1 3.0 61.7 10.2
1.04 1.13 0.96 1.05 0.91 0.94 0.8 I 0.81 0.83 0.70 0.82 0.63 0.80 0.84 0.8 1
0.33 0.33 0.20 0.27 0.30 0.19 0.32 0.13 0.23 0.31 0.24
0.42 0.62 0.37 0.44
Table 4. Results of femur F23. At some instances the elastic modulus could be determined, but not the compressive strength since the peak stress value was not reached. In the specimen number I denotes the most distal slab, 2 the next one,. . . until 5 the most proximal slab
2 0 %
II
g
7 5
755
Mechanical behaviour of cancellous bone Table 5. Maxima1 strength recorded in each femur
Femur
F31 F74
F23
F28
F67
aI(kg/mm2)
1.29 1.06
1.41
1.57 3.53
Correlations density
F8
among
mechanical
and bone mineral
properties.
The relation between the compressive strength or the modulus of elasticity and the wet and dry apparcorrelations ent density are highly significant (p < fKtO1 for the results of F31. F74 and the global results of the impact tested specimens). Differences in observed correlation coefficients between impact and slowly compressed femora are probably due to the different behaviour during compression. which will be discussed below. Since impact loading is the more realistic loading mode, the correlations among the properties of the impact tested femora should be regarded as the more meaningful. The correlation between the apparent density and the compressive strength upon impact loading indicates that the compressive strength is influenced by the density. However, since the correlation coefficient is considerably less than 1 (Table 7: 0.70 and 0.76), the density cannot completely account for the variation in compressive strength. Factors other than the density determine the strength level of the cancellous bone as well. It follows from the microscopic study that differences in strength observed at a given density are controlled to a large extent by the trabecular structure. The compressive strength increases with the thickness of the trabeculae parallel with the compression direction and the number of trabeculae perpendicular to the loading direction. Since it was found that failure occurred by a bending of the trabeculae, it is not
1.79
tribution of the joint load from the articular area of contact to the cortex of the femur. Burstein, Shaffer and Frankel (1970) showed by a mathematical model that, at least under static conditions, the trabecuiar bone of the condyles has an important load carrying task; 800,; of the surface loading is transmitted through the inner spongy bone. Hayes, Swenson and Schurmann (1975) clearly demonstrated by a finite element analysis that the stress in the cancellous bone diminishes with an increasing vertical distance to the joint. According to Wolfi’s law (1870) it can be readily assumed that the mechanical properties of the intracondylar cancellous bone will decrease likewise. In the medial condyle a higher compressive strength than in the lateral condyle was recorded. The highest value was reached posteriorly (see Fig. 5, the most distal specimens of slice 1). This result indicates that the larger part of the total joint reaction force is probably borne by the posterior medial condyle. The data obtained for the maximum compression strengths reached in the medial posterior condyle of each femur (Table 5) agree with previous data for the compressive strength of intracondylar cancellous bone of the femur and tibia with varying direction (Behrens. Walker and Shoji. 1974).
Table 6. Results of the linear regression analyses for the specimens of femur F23. Compressive stresses and elastic moduli are expressed in kg/mm*; strains in y:, Y
Al
X
R
P
Bmwchonm.
1977.
Vol.
IO.
pp.
141-162
Pergamon Press. Printed I” GreatBritain
THE MECHANICAL BEHAVIOUR OF INTRACONDYLAR CANCELLOUS BONE OF THE FEMUR AT DIFFERENT LOADING RATES* PAUL DUCHEYNE$, Luc HEYMAN$ MARC MARTENS, ETIENNEAERNOUDT. PAUL DE MEESTERand
JOZEFC. MULIER
Katholieke Universiteit te Leuven, Department of Metallurgy, B-3030 Heveriee and University Hospitals, B-3041 Pellenberg. Belgium Abstract-The compressive properties of human cancellous bone of the distal intracondylar femur in its wet condition were determined. Specimens were obtained from six cadaveric femora and were tested at a strain rate of 0.002, 0.10 and 9.16 see- i. It was found that the compressive strength decreases with an increasing vertical distance from the joint. The highest compressive strength level was recorded in the posterior medial condyle. Correlations among the mechanical properties, the bulk specimen density and the bone mineral content yield (i) highly significant correlations between the compressive strength and the elastic modulus (ii) highly significant correlations between the compressive strength or the modulus of elasticity and the bulk specimen density (iii) a doubtful correlation between the compressive strength and the bone mineral content. All recorded graphs of the impact loaded specimens displayed several well defined stress peaks, unlike the graphs recorded at low loading rates. It can be concluded that upon impact loading the localized trabecular failure which is associated with each peak, does not affect the spongy bone’s stress capacity in a detrimental way.
INTRODUCTION
Mechanical properties of bone have been studied intensively. Most research efforts have been devoted to the determination of the mechanical behaviour and characteristics of compact cortical bone. Some recent literature surveys account for the gathered knowledge
of the mechanical behaviour of cortical bone (Currey, 1970; Evans 1973; Reilly and Burstein 1974). The weight bearing bones of the human skeleton consist of an outer shell of compact cortical bone and an inner spongy structure of cancellous bone. The knowledge of the mechanical properties of the latter type can be considered as important for several reasons. Firstly, the cancellous bone is an integrated part of the bone as an anatomical structure. In order to describe the mechanical functioning of a bone, the mechanical properties of all its components including the cancelbus bone should be known. A recent example which pertains to this point is given by the work of Hayes, Swenson and Schurmann (1976) which suggests that the incidence and nature of tibia1 plateau fractures are influenced by the mechanical characteristics of the subchondral bone. Secondly, the knowledge of the mechanical properties of cancellous bone enhances the fundamental understanding of how cancellous bone behaves upon loading and clarifies the relationship among mechanical properties, mechanical behaviour and trabecular structure. Thirdly, since total joint replacement prostheses are mainly in contact with trabecular bone, improve* Received 23 February 1917. Present address: (Sept. 1976Aug.
t
1977) Department of Materials Science and Engineering, University of Florida, Gainesville, FL 32611, U.S.A. 747
ments of the functioning and the design of present prostheses rely upon the exact and accurate knowledge of cancellous bone properties. The current development of new prosthetic devices with bone ingrowth at the interface demands for a good understanding of the trabecular bone properties. The compressive strength properties of cancellous bone which have been determined most frequently are those of human vertebral spongy bone. These data were summarized by Evans (1973). However, with respect to prosthetic total joint replacements the knowledge of the mechanical behaviour of the cancellous bone of long bones should be readily availabie. Directional differences of the compressive strength and the modulus of elasticity for different trabecular regions of a human femur were reported by Knese (1958). Behrens, Walker and Shoji (1974) studied the cancellous bone of several normal and arthritic knees. Parameters which were included in their study were the orientation and position of the specimens, the bulk specimen density, the linear absorption coefficient and the bone material density. Schoenfeld, Lautenschlager and Meyer (1974) determined the ultimate compressive strength and the stress relaxation of human cancellous bone from the femoral head. Their specimens were obtained from femoral heads removed at surgery for total hip joint replacement. From their report it is not clear whether the cancellous bone was healthy. Pugh, Rose and Radin (1973a and b) studied the elastic and viscoelastic properties of human subchondral cancellous bone of the femoral condyles and established a relationship between mechanical properties and trabecular structure. The present paper deals with the compressive properties of human cancellous bone of the distal in-
748
PAUL DUCHEYNE et a[.
tracondylar femur. The compressive strength and the elastic modulus of cylindrical hone samples were determined by compressive tests at both low and impact loading rates. Since bones are subjected in uiuo to a high loading rate, it is essential to test spongy bone samples at a high loading rate to obtain valuable data on the compressive strength and elastic modulus of cancellous bone. Tests at low loading rates were also included in this study in order to compare the mechanical behaviour of cancellous bone at a physiological loading rate with the behaviour at rates commonly used by others (Galante, Rostoker and Ray, 1970; Schoenfeld, Lautenschlager and Meyer, 1974; Behrens, Walker and Shoji, 1974). Correlations among the mechanical properties and the bulk specimen density, the position, the bone mineral content and the trabecular structure were attempted. METHODS
Sawing of the blocks into slabs
I lMilling of the,slab surfacesl
I
Drilling of cylindrical bone SaDhS
I
I
AND MATERIALS
A
Figure 1 details the successive steps followed during the preparation of the specimens. The study was performed on human autopsy material, which was stored in a deep freeze at - 35°C until specimen preparation. The autopsy subjects included 2 females and 4 males, ranging in age from 43 to 77 yr. Data on the age, sex and physical activity of the patients are summarized in Table 1. There was no history of bone or joint disease, which was confirmed by radiographic examination.
IDrying and defatting of
the samplcs~
Density measurements
*
Preparation of the compression specimens
The distal femoral epiphyses were embedded in foam and the position of the femurs in the surrounding foam block was determined radiographically. This technique provides reproducible slabs from the distal epiphyses, parallel with a plane tangential to the condyles. Five slabs with a thickness of about 8 mm were sawn from each femur. In order to assure parallel surfaces, the slabs were milled at -32°C. Only at this or lower freezing temperatures one can expect not to damage the trabeculae upon milling. Core drills with an inner diameter of 5 mm were used to cut cylindrical specimens. Vertically oriented specimens were obtained. The localization of the specimens was chosen to cover a range of varying radiographical density. Figure 2 shows the second slab of femur F28 before and after removal of the specimens. During preparation the specimens
Fig. 1. The subsequent steps of the specimen preparation. were kept wet constantly and preserved at -32°C between successive steps. Table 2 represents the total number of specimens per femur. Volume and density measurements
Prior to the mechanical tests, the diameter and the length of each specimen was determined using a Cambridge measuring microscope. The samples were weighed subsequently. These data allow the calculation of the wet apparent bulk density (a,), which is defined by the wet sample weight divided by the total sample volume. The compression tests
Two femurs (F31 and F74) were tested in compression on an Instron TT-DM-L testing machine at a
Table 1. Data on the obtained femurs Femur number
Age
F31 F74 F23 F28 F67 F8
63 49 47 77 65 43
Sex
M M
Physical activity information not obtained heavy work p&t office worker heavy work in the mines information not obtained housework
Femur
Loading rate (cm/min)
Strain rate W-V
left left right left right right
0.1 5 440 440 440 440
0.002 0.10 9.16 9.16 9.16 9.16
749
Fig. 2. The second slab of femur F28 before and after removal of the cylindrical specimens.
Fig. 3. The high loading rate testing device. The cancellous bone specimen can be seen on the lower fixture and is surrounded by a steel ring. The extensometu is attached to the same fixture.
Mechanical behaviour of cancellous bone Table 2. Number of specimens per femur Femur
F31
Numberofspecimens 42
F74 F23 F28 42
25
24
F67
F8
25
25
loading rate of 0.1 and 5 cm/min. The recorder chart was driven at different constant speeds to obtain a 45 degree slope during the elastic deformation. Each test was performed within two minutes of air exposure of the specimen. The samples of the other four femurs (F23, F28, F67 and F8) were tested at a high loading rate @Ocm/min) on a different, hydraulically operating testing device (see Fig. 3). The specimens were positioned on the extension of the upwards moving piston and compressed against the upper die. The bone specimens were surrounded by a steel ring, which at the end of the test stopped the upward motion of the piston by the release of the hydraulic energy into elastic deformation of the ring. These rings, ground to a precise height, made it possible to compress the specimens over a predetermined length yielding deformations in the range of 5-15%. The microscopic structure of the tested specimens could still be examined, as only limited amounts of damage were permitted. The displacement was measured with an extensometer based on the principle of magnetic inductance varying with the position of a central movable pin. The signals from the load transducer and the extensometer were recorded on an analogdigital recorder (Biomation Waveform Recorder, model 1015) and, for storage purposes, on a seven channel tape recorder (Philips, ana-log 7). Load-deIIection curves were plotted on an x-y recorder (Honeywell, model 550) using the output of the analogdigital recorder. Density measurements After compression testing the specimens were defatted ultrasonically for 2 hr in a 50% ether-5004 ethanol solution. They were allowed to dry for 24 hr at 55°C. This was followed by the determination of the dry apparent bulk density (6,) defined by the dry sample weight divided by the total sample volume. Examination of the structure In order to study the failure mechanisms and the relationship among trabecular structures, mechanical properties and apparent density, twenty eight impact loaded specimens were selected and embedded in an epoxy resin (Technovit) or in methyl methacrylate. As several peaks could appear in the loaddeformation graphs, specimens with the same density displaying curves with a different number of peaks were selected. Apart from the choice. of specimens following this main criterion, specimens were selected on the basis of some secondary criteria: the variation of the density (F28 and F8), the strain at the top of the second peak (F67) and the variation of the modulus of elasticity (F23).
751
The specimens were cut parallel with their longitudinal axis by the use of a low deformation, precision saw with a diamond blade (Buehler: Isomet). After polishing the structure was examined on a reflected light microscope (Neophot 2-Jena). Bone mineral content determination The bone mineral content of 29 samples was determined by ashing at 500°C for 48 hr and subsequent weighing. The experimental absolute error on the bone mineral content was assessed on the basis of double independent measurements of the dry specimen weight and the ash weight; the differences between the two independent measurements were considered the absolute errors on these variables; the absolute error of the bone mineral content was calculated using these absolute errors on dry specimen and ash weight.
RESULTS The compression
tests at the lower loading rates
A typical recorded graph of a compression test at a loading rate of 5 cm/min is shown in Fig. 4. Once the peak value is reached a stepwise decrease of the load is observed. The peak value is considered to be the compressive strength a; the elastic modulus E is determined by the constant slope of the initial loadtime curve. The compressive strength was correlated with the elastic modulus, the wet apparent bulk specimen density (6,) and the apparent density after drying and defatting (6,). Linear regression analyses yield the results which are summarized in Table 3. A, and A2 are the constants of the linear relation Y= A, + A2X. R is the correlation coefficient, a value close to 1 indicating a high degree of correlation. K is the number of representation points used for the particular regression and YM and XM are the mean values of the Y and X parameters. High positive correlations @ < 0.001) were noted for all relations tested. The variation of the compressive strength with the location of the cancellous bone specimens is shown in Fig. 5. The strongest region was found to be the medial posterior side. The specimens removed from the more distal slabs, proved to be stronger. It is important to notice that the fifth slab usually did not include the condyles. The compression tests at an impact loading rate A typical recorded curve of a compression test at a loading rate of 44Ocm/min is represented in Fig. 6. All recorded graphs display several well defined peaks; the top values of the peaks were considered as consecutive compressive strengths er, c2.. . . . The elastic modulus (E,, El,. . .) was determined as the constant slope of the stress-strain curves. The strain,
752
PAULDUCHEYNE et al. b
-P
7J
u 0
time
Fig. 4. A schematical load-time curve of a sample tested
at a loading rate of 5 cm/min.
The results of the linear regression analyses indicate the existence of a significant correlation between compressive strength and wet and dry apparent bulk specimen density (Fig. 7). The correlations between the elastic modulus and the wet and dry apparent density were found to vary in the same way as the correlation among compressive strength and wet and dry apparent densities. No significant correlation between the compressive strength and the strain at peak values was found. Neither could a significant correlation be established between the strain at the peak values and the apparent bulk specimen density. The strain at the different peaks could, however, be correlated with each other. The regression relating the compressive strength to the elastic modulus is highly significant: Fig. 8 @ < 0.001). Plotting the consecutive compressive strengths against each other, a highly significant correlation was obtained (p < 0.001). The equations u, = o2 and o1 = o3 lie within the 99% confidence limit of the established correlations, except for values of u1 lower than 0.50 kg/mm2 in the correlation between g1 and u2: Fig. 9.
corresponding with the peak values was also calculated (PI, Pt, . . . .). Similar to the spongy bone specimens tested at the lower loading rates, the testing at high loading rates revealed a wide variation of the tist compressive strength with regard to the specimen’s location. The relation between location and compressive strength shows the same apparent tendencies for all loading rates used. ‘Most spongy bone specimens have a compressive strength in the range of 0.10-2.30 kg/mm2 and the value of the elastic modulus is mainly between 6 and 300 kg/mm*. As an example, the results of F23 are listed in Table 4. The highest recorded values of the compressive strength for all femurs are represented in Table 5. The compression stresses associated with the different peaks (gal, Q~,. . . .) were correlated with their elastic modulus (E,, El,. . . .) and strain at the peak value. Correlations with the apparent wet (8,) and dry (c&-j bulk specimen density were attempted as well. The experimental results were correlated for each femur separately and for the four femurs together. The correlations covering data points of all 4 femurs, are called the global correlations. As an example the results of the linear regression analyses of F23 are presented in Table 6. The correlation coefficient and the number of representation points of the global analyses are compiled in Table 7. The relations between the compressive strength, and .the apparent bulk densities are plotted on Fig. 7, the relation between the elastic modulus and the compressive strength in Fig. 8 and the relation between first and second com- Fig. 5. The variation of the compressive strength (expressed in kg/mm’) with the position (F74). pressive strength in Fig. 9. Table 3. Results of the linear regression analysis for the specimens tested at the lower loading rates. The compressive strength and the elastic modulus are expressed in kg/mm* Y
F31 (0.1cm/min)
A2
X
R
K
XM
YM
d
0.01 2.102 2.232
E
- 2.05 -0.378
6. s,
0.78 0.80 0.88
36 42 42
38.02 1.22 0.41
0.61 0.56 0.56
u u u
- 0.022 - 1.85 -0.33
0.03 1.993 1.974
0.84 0.87 0.83
36 38 38
15.09 1.08 0.34
0.36 0.36 0.36
u a
F74 (5 cm/min)
Al 0.216
Mechanical behaviour of cancellous bone
2.69
I
nw 1
6.99
1
strain
[%I
Fig. 6. The stress-strain curve of a specimen tested at a loading rate of 440cm/min.
reaction force reaches a peak at heel strike and toeoff. At that moment the angle between the joint reaction force and the femoral axis is approx. 20”. Behrens, Walker. and Shoji (1974) who have studied the variation of the compressive strength of intracondylar cancellous bone with a variation in angular position with regard to the femoral axis, have suggested that the highest compressive strength would have been recorded with specimens oriented under an angle of 20” with the femoral axis. Since the orientation of our tested compression specimens approaches the orientation of the peak force at walking and presumably the orientation of maximum strength, differences in strength due to varying location can be interpreted on the basis of the actual functioning of the intracondylar trabecular bone. No statistical analysis on the relation between location and compressive strength was performed. Due to differences in physical activity, the compressive strength at functionally equivalent locations of femurs of different individuals can vary by a factor 2 to 3. This variation is superposed on the variation with the location within each femur. Furthermore, it is very uncertain whether bone specimens were obtained DlSClJS!SlON in identical functional locations. Comparing the The irzfluence of the location strength within each femur location by location and The compressive strengths measured in this study observing identical trends within each femur is more meaningful than comparing the mean value of all yield a map of the strength of intracondylar cancellous bone of the femur at an orientation parallel to femurs for each location. As a matter of fact the stanthe vertical joint reaction force at stance phase. This dard deviation on the mean compressive strength is direction is not the one at which the highest peak so large due to differences between individuals that the statistical analysis performed in this way would loads are reached during activities such as walking and climbing and descending stairs. It is however reject a significant variation with location. From the results it follows that the compressive close to the direction of the peak forces during the most frequent daily activity with a considerable resul- strength decreases with increasing vertical distance to tant loading, which is walking. In fact, the results of the joint. This is not surprising since the main ~~~ mechanical function of the trabecular bone is the disMorrison (1968) indicate that durinn walkine the ioint .
The microscopic examination of sections parallel to the compression direction revealed some striking variations of trabecular patterns. The weaker specimens were composed of columnar arrangements of trabeculae; the stronger samples displayed a branched trabecular structure. Comparing specimens with the same density but a different compressive strength, it was found that the stronger specimens had thicker and more branched trabeculae. Any sample which was tested beyond its first compressive strength showed structural damage of the trabeculae. Trabeculae failed by transverse splitting (Fig. 1Oa)or by shearing (Fig. lob) of their lamellae. The bone mineral content, determined by ashing varied between 62 and 70%. The absolute error on the bone mineral content was assessed to be 0.33% at the mean, with S.D. of 0.21%. When plotting the bone mineral content against the compressive strength ui a poor correlation was obtained. The level of significance was p < 0.1 and the correlation coefficient 0.28. Figure 11 shows the large scatter of representation points of this relation.
I
2’: 2Y 22 3B 3D 4A 4B 4D 4E SB SC
1C IE IZ
Specimen number
1.12 1.33 0.69 0.91 0.07 0.37 0.45 0.35 0.60 0.14 0.40 0.87 0.07
0.60
I.41
169.4 23.3 88.6 152.8 39.8 13.5 1.9 19.0 22.7 17.3 31.2 5.3 19.8 67.8 4.8
1.99 6.22 3.13 2.57 3.12 2.59 8.18 4.60 3.51 3.91 3.64 4.07 3.50 2.26 2.27 1.43 1.07 1.45 0.78 1.07 0.11 0.37 0.69 0.24 0.76 0.04 0.37 0.75 0.07 z 97:6 32.2 72.9 4.2 29.7 29.2 10.4 16.9 2.6 9.2 79.8 3.8
105.9
4.13 5.68 4.87 7.96 6.99 12.70 9.81 7.47 9.18 6.48 15.04 7.44 6.51 5.55 0.27 0.79 0.06
0.87
-
-
12.64 13.81 11.43 15.33 12.65 13.11 10.96 IO.10
69.7 14.7 18.6 35.1 23.3 28.1 3.0 61.7 10.2
1.04 1.13 0.96 1.05 0.91 0.94 0.8 I 0.81 0.83 0.70 0.82 0.63 0.80 0.84 0.8 1
0.33 0.33 0.20 0.27 0.30 0.19 0.32 0.13 0.23 0.31 0.24
0.42 0.62 0.37 0.44
Table 4. Results of femur F23. At some instances the elastic modulus could be determined, but not the compressive strength since the peak stress value was not reached. In the specimen number I denotes the most distal slab, 2 the next one,. . . until 5 the most proximal slab
2 0 %
II
g
7 5
755
Mechanical behaviour of cancellous bone Table 5. Maxima1 strength recorded in each femur
Femur
F31 F74
F23
F28
F67
aI(kg/mm2)
1.29 1.06
1.41
1.57 3.53
Correlations density
F8
among
mechanical
and bone mineral
properties.
The relation between the compressive strength or the modulus of elasticity and the wet and dry apparcorrelations ent density are highly significant (p < fKtO1 for the results of F31. F74 and the global results of the impact tested specimens). Differences in observed correlation coefficients between impact and slowly compressed femora are probably due to the different behaviour during compression. which will be discussed below. Since impact loading is the more realistic loading mode, the correlations among the properties of the impact tested femora should be regarded as the more meaningful. The correlation between the apparent density and the compressive strength upon impact loading indicates that the compressive strength is influenced by the density. However, since the correlation coefficient is considerably less than 1 (Table 7: 0.70 and 0.76), the density cannot completely account for the variation in compressive strength. Factors other than the density determine the strength level of the cancellous bone as well. It follows from the microscopic study that differences in strength observed at a given density are controlled to a large extent by the trabecular structure. The compressive strength increases with the thickness of the trabeculae parallel with the compression direction and the number of trabeculae perpendicular to the loading direction. Since it was found that failure occurred by a bending of the trabeculae, it is not
1.79
tribution of the joint load from the articular area of contact to the cortex of the femur. Burstein, Shaffer and Frankel (1970) showed by a mathematical model that, at least under static conditions, the trabecuiar bone of the condyles has an important load carrying task; 800,; of the surface loading is transmitted through the inner spongy bone. Hayes, Swenson and Schurmann (1975) clearly demonstrated by a finite element analysis that the stress in the cancellous bone diminishes with an increasing vertical distance to the joint. According to Wolfi’s law (1870) it can be readily assumed that the mechanical properties of the intracondylar cancellous bone will decrease likewise. In the medial condyle a higher compressive strength than in the lateral condyle was recorded. The highest value was reached posteriorly (see Fig. 5, the most distal specimens of slice 1). This result indicates that the larger part of the total joint reaction force is probably borne by the posterior medial condyle. The data obtained for the maximum compression strengths reached in the medial posterior condyle of each femur (Table 5) agree with previous data for the compressive strength of intracondylar cancellous bone of the femur and tibia with varying direction (Behrens. Walker and Shoji. 1974).
Table 6. Results of the linear regression analyses for the specimens of femur F23. Compressive stresses and elastic moduli are expressed in kg/mm*; strains in y:, Y
Al
X
R
P
