Journal of Biomechanics 31 (1998) 741—745

Representative assessment of long bone shaft biomechanical properties: an optimized testing method Jos A.M. Bramer!,*, Robbert H Barentsen", Maarten vd Elst!, Elly S.M. de Lange#, Peter Patka!, Henk J.Th.M. Haarman! ! Department of Traumatology, University Hospital Vrije Universiteit, Amsterdam, The Netherlands " Department of Clinical Physics and Engineering, University Hospital Vrije Universiteit, Amsterdam, The Netherlands # Department of Epidemiology and Biostatistics, University Hospital Vrije Universiteit, Amsterdam, The Netherlands Received in final form 17 June 1998

Abstract Whole bone bending tests are commonly used in mechanical evaluation of long bones. Reliable information about the midshaft can only be obtained if the bending moment is uniformly distributed along the shaft, and if the distribution of the bending stress is not adversely influenced by rigid clamping of the bone ends. A testing device was developed to determine bending stiffness of long bones in 24 directions, perpendicular to the bone axis. For optimal distribution of bending moment and stress, four-point bending was performed, and bone ends were simply supported, not rigidly clamped. The method was validated by repeated testing of a stainless steel rod, and a sheep femur. Left—right ratios were assessed twice in 2 groups of 5 sheep: one control group, and one group in which the left femur was stabilized with a stainless steel interlocking nail for 2.5 yr, after a midshaft osteotomy. Test results obtained with the steel rod reproducibly were close to predicted values. Measurements with the sheep femurs were reproducible and precise for 3 of the 4 parameters of the bending test. Stiffness parameters were significantly higher in the operated sheep than in the control group. We conclude that the method described here provides accurate and reproducible information, which is representative for the long bone shaft. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Animal experiments; Long bone shaft; Mechanics; Four-point bending; Stress distribution

1. Introduction The rigidity of long bones reveals differences if bending tests are done in several directions of the transverse plane (Ruff and Hayes, 1983; Lovejoy et al., 1976). These differences are even more pronounced after fracture fixation (Foux et al., 1993). Foux developed a method to assess the distribution of the bone rigidity by performing threepoint bending tests in 24 directions perpendicular to the bone axis (Foux et al., 1990). A disadvantage of threepoint bending tests is the local deformation of the bone at the site where the force is applied, resulting in an underestimation of the Young’s modulus (Turner, 1993). Moreover, the bending moment is maximal at this site, which will have a major effect on the test results. If a four-point

* Corresponding author. Tel.: 31-20-6151301; fax: 31-20-6151301. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S0021-9290(98)00101-8

bending test is used, the bending moment will be uniform between the applied forces (Fig. 1) and the weakest part of the shaft will determine the outcome of the test (Timoshenko and Goudier, 1970). Moreover, the influence of shearing force will be reduced (Torzilli et al., 1981). Furthermore, test results will be influenced by the method of fixating the bone ends in the testing device. The theory of elasticity shows that rigid clamping of a beam in a bending device, will result in maximal stress near the points of fixation, and minimal stress in the middle. More appropriate distribution of the stress, with the maximum in the middle, will be achieved if the ends are allowed translation in the plane perpendicular to the plane of bending (Fig. 2) (Timoshenko and Goudier, 1970; Griffel, 1966). In this report we describe a device for the assessment of the rigidity of long bones in a four-point bending test in 24 planes, in which the bone ends are not rigidly fixed but simply supported. This results in a uniform distribution

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Fig. 1. Bending moment distribution along the length of a beam in three- and four-point bending.

Fig. 2. Bending stress distribution along the length of a beam in case of fixated and simply supported ends.

of the bending moment, and a more appropriate distribution of the bending stress along the shaft.

deformation was introduced. After each test the cups were taken out of the rings, turned 15° and placed in the device again for the next test. This was repeated 24 times, untill a full revolution was made.

2. Device design The long bone was placed with the ends in cylindrical metal cups. The axis was centred. Fixation took place by filling the cups with a low melting point Bismuth alloy (A 301, Degussa, Wolfgang, Germany; melting point 47°C) in the liquid state. The outside of the cups consisted of 24 small facets, corresponding with the 24 facets of the rings in which they were placed (Fig. 3). These rings had a lug on two sides which was placed on a saddle. The device was positioned on a bending machine (Hounsfield H5000M, Hounsfield Test Equipment, England) which recorded load and deflection. A four-point bending test was performed by applying two equal forces at the edges of both cups. The cups were allowed translation in the horizontal plane perpendicular to the plane of bending. Bending was performed with a constant crosshead speed of 1 mm/minute. Deflection was measured at the probe where the bending machine applied the force (F in Fig. 3). The test was nondestructive, no plastic

3. Validation of the method The method was validated in four experimental settings: (A) A stainless-steel rod (asi no. 316), with a diameter of 8 mm, was tested 5 times in the device. (B) The entire procedure, including fixation of the bone ends in the cups, and mounting of the device, was repeated 4 times with one sheep femur. (C) Both femurs of five healthy adult sheep (controls) were tested to assess left—right differences. The entire procedure was repeated for a second time to assess reproducibility of the method (duplo tests). (D) Both femurs of five operated sheep were tested. These sheep received a stainless-steel interlocking nail 2.5 yr earlier stabilizing a midshaft osteotomy of the left femur. Before testing, the nail was removed. Four femurs of two sheep were tested twice (duplo tests).

J.A.M. Bramer et al. / Journal of Biomechanics 31 (1998) 741—745

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where x is the distance from the center of the lug to the point where the force was applied, y half the length of the long bone shaft, F the applied bending force, d the displacement of the probe and I the moment of inertia. For each femur the 24 EI-values were plotted in polar coordinates and elliptical regression analyses was performed, resulting in an ellipse. The ellipses of both femurs of one sheep were plotted in the same coordinate set, centralized and the ellipse of the right femur was mirrored in the ½-axis. With the use of semimajor axis (a), semiminor axis (b), and angle of inclination (a) of both ellipses (Fig. 4), the following parameters were calculated: Stiffness index:

C

SI"

EItestbone EIcontralateral

D

. minimal

This is the ratio of the stiffness of the testbone versus the contralateral bone in the direction in which this ratio is minimal. Fig. 3. Device for bending test in 24 directions: (1) tested bone; (2) metal cups and (3) corresponding rings; (4) lug at the side of the rings; (5) saddle; (6) testprobes for applying force.

All tests were performed 8 weeks after the sheep were sacrificed. The femora were stored in 70% alcohol, and kept wet during testing (Linde and Sorensen, 1993). All experiments were approved by the DEC (Animal Experiment Committee) and carried out in accordance with the Dutch regulations of Animal Welfare.

4. Processing of the test results

Area ratio: (ab)testbone AR" . (ab)contralateral This ratio represents the ‘total stiffness’ of the testbone, as compared to the contralateral bone. Flatness ratio: (b/a)testbone FR" . (b/a)contralateral This represents the relative distribution of the stiffness of the bone in different directions. Inclination difference:

After linear regression on the load—deflection curves, 24 load—deflection quotients were obtained for each femur. Because the main contents of the cups consisted of the bismuth alloy, the elasticity of the alloy (4]109 N m~2) was assumed for this part of the device. The flexural rigidity (EI) of the bone in every direction tested could be determined by the following equation, derived from beam theory. Equation for calculating flexural stiffness (EI): 1 Fx2y 1 Fx3 d" 2 # 2 (EI)bone 3(EI)cups

(EI)

bone

"

[F/d]1@2x2y F x3 1! d 6(EI) cup3

C CD

D

ID"atestbone!acontralateral . This is the difference between the angles the semiminor axis make with the anterior—posterior plane.

5. Results (A) In repeated testing of the steel rod in the device, the mean value of flexural stiffness was

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Fig. 4. Ellipses of both femurs of operated sheep no. 4, plotted in the same set of coordinates. a"semi-major axis (e.g. 93.5 N m2 for the left, and 71.4 N m2 for the right femur) b"semi-minor axis (e.g. 86.4 N m2 for the left, and 68.4 N m2 for the right femur). a"angle of the semi-minor axis with AP-plane (inclination) (e.g. 145.62° for the left, and 122.7° for the right femur).

31.98 N m2 (standard deviation 2.02), whereas the calculated theoretical value was 35.39 N m2. (B) Repeated performance of the test with one sheep femur resulted in mean values of 108.30 N m2 for the semimajor axis (S.D. 4.04), and 101.25 N m2 for the semiminor axis (S.D. 4.15) of the ellipse. The mean area was 109.72 N2m4 (S.D. 7.39), and the mean flatness was 0.94 (S.D. 0.04). Inclination showed a mean value of 123.00° (SD 49.99). (C)/(D) In the bending tests with the control sheep, the Stiffness Index, Area Ratio, and Flatness Ratio all approached 1, as expected (Table 1). In the operated sheep, the stiffness index and the aria ratio were significantly higher (p"0.009, Mann— Whitney test). The flatness Ratio in the operated sheep approached 1, not differing from this value in the control group (p"0.917). The Inclination difference appeared to be highly variable within the two test groups, and the difference between these groups was not significant (p"0.754). From the seven duplo tests of five control and two operated sheep, the standard deviation of the difference of the duplo, and the repeatability coefficient were calculated for each parameter (Bland and Altman, 1986).

For the Stiffness Index, Area Ratio, and Flatness Ratio the standard deviations were acceptable (0.07, 0.15, and 0.04, respectively) as were the repeatability coefficients (0.14, 0.30, and 0.08). However, the standard deviation and repeatability coefficient of the inclination difference were extremely high (64.27 and 128.54).

6. Discussion In vivo, long bones are mostly exposed to torsion and bending forces (Ruff and Hayes, 1983; Raftoupoulos and Qassem, 1983; Bertram and Biewener, 1988), representing the most common cause of long bone fractures (Lovejoy et al., 1976; Evans et al., 1951; Alms, 1961). The majority of fractures occur in the middle third of the shaft (Dencker, 1965). Biomechanical evaluation in animal experiments should produce accurate information about the whole shaft, especially the middle third. In the presented method this was achieved by using a four-point bending test without rigid fixation of the bone ends. This way the bending moment was uniform along the whole length of the shaft, and the bending stress was maximal in the shaft between the applied forces, and minimal at the proximal and distal ends. No

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local deformation of the midshaft was introduced, because the loads were not applied directly to the bone. The stiffness index, area ratio, and flatness ratio proved to be useful in comparing left—right differences in different groups of animals. These ratios approached 1 in the control group, indicating no difference between left and right femur. This symmetry of mechanical properties was demonstrated before (Kersey et al., 1994; Mather, 1967; Sumner et al., 1988). It results in the contralateral femur being the ideal control. The stiffness index and area ratio were significantly higher in the operated sheep. The flatness ratio approached 1 in both the controls and the operated sheep, meaning that there was no preferential direction of rigidity. This might be explained by the intramedullary fixation of the fractures used here, making stress shielding and other possible effects similar in all directions. In the duplo tests, the stiffness index, the area ratio, and the flatness ratio appeared to be very reproducible. The inclination difference showed a large variation and a poor reproducibility, which might be explained by the fact that the flatness ratio always approached 1. This means that the ellipse of each bone approached a circle, making inaccuracy in assessment of the direction of the semiminor axis more likely. If there is no preferential direction of the stiffness, the inclination difference seems not a very relevant parameter. However, if flatness ratios would not equal 1, this parameter might produce more reproducible and useful results. We conclude that the described method accurately and reproducibly determines mechanical properties of the long bone shaft. By optimal distribution of bending moment and bending stress, appropriate information can be obtained about the complete shaft. Acknowledgements The authors wish to acknowledge the Biomaterials Group of the University of Leiden, the Netherlands, Klaas Boshuizen of the Dept. of Clinical Physics and Engineering, and Ger Vink and the other workers of the Clinical Animal Experimental Laboratory of the Vrije Universiteit Amsterdam for their support in this study.

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