Mechanical Properties of Bone

Rabbit femora and ulnae were tested to fracture in a torsion loading experiment. Various mechanical parameters were determined under five loading rates ranging from 0.003 to 13.2 radians per second. The maxin.im torque, maximum torsional deformation, energy absorbed to fracture, and torsional stiffness all increased with the rate of deformation, reached a maxinaim, and then declined. The bones absorbed 67 per cent more energy, had 33 per cent more torque and torsional deformation, and 5 per cent more stiffness at the highest rate of deformation as cornpared with the lowest. Strength of the bone, a term frequently used clinically, represents to a mechanical engineer a generic term which is imprecise. It may presume that one or many of the numerous and complex mechanical testing methods are applicable and show consistent results, or it may be so general as to have no precise meaning. Because bone shows viscoelastic behavior, it has neither a single stress-strain curve nor a single characteristic for ultimate failure. With different testing conditions, such as in tensile tests, there may be a family of curves; several criteria may be available for assessment of failure, and different characteristic values may be obtained depending on the test circumstances. The physical properties of bone as tested are time dependent, that is, depend on the rate of loading so that the crucial variable of rate of deformation must be included in any analysis of its behavior. The slow skier fractures his tibia at a different rate of deformation than the fast skier. The halfback who sustains a fractured femur because a I 30-kilogram linebacker falls on his leg has his bone fail at one rate of deformation. If the same halfback had a collision while driving his sports car at seventy kilometers per hour and fractured his femur, the bone would have failed at a much faster rate of deformation. In the case of high speed accidents like automobile collisions and some ski fractures, it is obvious that bones fail at very rapid rates of deformation. However, even in an ordinary case of a slow fall, the rate of deformation may still be quite fast. For example, a person falls from the standing position to the lying position on the ground. He breaks his fall by landing on the palm of his hand, thus twisting his humerus. Assuming that his center of gravity was displaced one meter in the vertical direction toward the floor, this would give his hand a colliding speed of 4.4 meters per second. If we estimate that the length of the forearm is 0.25 meter and that the humerus will fail with 20 degrees of twist, the application of the load to the humerus lasts 0.015 second. Experiments on the breaking strength of bone should be designed so as to give information that can be meaningfully related to the rate of deformation, and we have attempted to do this in the study we are reporting. * This work supported by the Yale Trauma Program and The Commonwealth Fund of New York, Fluid Grant PHS-RR-05358-09, Training Grant PHS-5-T0l-AM-05416-09, and the Crippled Children’s Aid Society. t Section of Orthopaedic Surgery, Yale University School of Medicine, New Haven, Connecticut 06510. 322 THE JOURNAL OF BONE AND JOINT SURGERY MECHANICAL PROPERTIES OF BONE 323 Many experiments for determining mechanical properties of bone have been performed at slow or undefined rates of loading, as shown in two recent review artides 2,3 Currey emphasized the need for high rates of loading, and stated that “all the static tests reported . . . could with advantage be repeated at high, controlled, loading rates. “ To our knowledge, there have only been three recent studies which have carried out investigations on the mechanical properties of bone at high, controlled rates of loading. McElhaney and Byars performed a series ofcompression experiments on small specimens, rectangular in cross section, of human and bovine femora under a wide range of rates of loading. Burstein and Frankel and Sammarco and associates tested whole human and canine bones in torsion at two rates of deformation. The purpose of the present paper is to portray the behavior of whole bones at five widely varying rates of deformation. Material and Method We chose a torsional method of loading for reasons of expedience. The rate at which a bone is torsionally deformed is defined either by strain rate or the rate of torsional deformation. The rate of torsional deformation is defined as the rate at which one end of the bone is twisted with respect to the other end. Torsional deformation is much easier to measure than strain rate because the geometry of a bone is so complex in cross section. The dimension is radians (or degrees) per second. The five different rates of torsional deformation chosen were in a range such that the slowest and the fastest fracture times were approximately I 20 seconds and 0.02 second respectively. The latter is faster than the ski-fracture loading rates suggested in the literature . The three intermediate rates divided the range between the slowest and the fastest rate in equal parts on a logarithmic scale. The bone to be tested was wrapped in a paper towel soaked with Ringer’s lactate solution and its ends were molded in epoxy resin. The apparatus used was a torsion testing machine (A. H. Burstein, Shaker Heights, Ohio) and a dual-beam oscilloscope (Taktronix Type 56 1 B). For the two fastest rates of application of force, the loading of the bone was achieved by a falling pendulum which engaged one end of the bone just before reaching the bottom position. Transducers were provided to measure the torque and torsional deformation. A microswitch, activated by the falling pendulum, triggered the oscilloscope sweep just before the bone started to load. The torque which was being applied and the angle of deformation produced were depicted on the vertical axis of the oscilloscope screen as related to time on the horizontal axis. For the slowest rate of loading, the pendulum was replaced by a lever, one end of which was attached to the bone and the other to a hanging weight and the loading rate was controlled by increasing the weight at a constant rate. The two intermediate rates of loading were obtained by a motor-screw-lever system. The rates of torsional deformation in radians per second (or in degrees per second in parentheses) were 0.003 (0. 1 7), 0.070 (4), 0.434 (23), 3.30 ( I 90), and 1 3.2 (750). Hereafter these deformation rates are represented by numbers 1 to 5, respectively. To get an estimate of the corresponding strain rate, one should multiply these rates by a factor equal to the average radius of the bones divided by the average bone lengths. This calculation gives a figure for the conversion factor, for the bones used in this experiment, of 0. 1. Limbs of thirty-four female adult rabbits were collected within one hour of death. Soft tissue was removed, and the bones were labeled, paired, and deep frozen in plastic bags at 20 degrees centigrade. It has been established that freezing has no effect on the mechanical properties of bone 6 The bones tested were femora and ulnae, with right and left sides constituting a pair. All the bone pairs available were randomly divided into four groups of approximately equal size. Each group was in VOL. 55-A, NO. 2, MARCH 1973