Journal of Orthopaedic Research 8 8 5 1 4 5 5 Raven Press, Ltd., New York 0 1990 Orthopaedic Research Society
Torsional Strength Reduction Due to Cortical Defects in Bone Bradley C. Edgerton, Kai-Nan An, and Bernard F. Morrey Biomechanics Laboratory, Department of Orthopaedics, Mayo CliniclMayo Foundation, Rochester, Minnesota, U.S.A.
Summary: This study correlated torsional strength reduction with circular defect size in cortical bone, to define the “stress riser” and “open-section’’ effect of the defects. The experimental model was developed and verified. Circular defects from 10 to 60% of bone diameter were then created in paired sheep femora and the bones loaded to failure. Contrary to theory, this experimental study suggests that small defects (10%) of bone diameter cause no significant torsional strength reduction. A 20% defect caused a 34% decrease in strength, representing the “stress riser” dimension. Defects between 20 and 60% of bone diameter decreased strength linearly as a function of defect size, and thus no discrete “open section” dimension was identified. For circular defects, we were unable to demonstrate a discrete “open-section’’ effect at which dramatic strength reduction is observed. These data may prove to be helpful when planning surgery that involves placing defects in bone such as for infection, biopsy, and prosthesis removal. The accepted guideline to avoid defects of greater than 50% of the bone diameter may be too great. Our data reveal this 62% reduction in torque strength and 88% energy to failure exist with a 50% circular defect. Key Words: Cortical bone-Torsional strengthCircular defect.
The complications occurring because of cortical defects in bone are well recognized in the clinical practice of orthopaedics. Whether due to biopsy, tumor, or internal fixation, these defects frequently lead to pathologic fracture (6,7,10,16,19). In contrast to their clinical relevance, little experimental data exist correlating defect size with strength reduction in cortical bone. The engineering literature, however, does provide detailed information about material irregularities, and two classes of defects have been described (15,17,20,22). A hole of infinitely small size, a “stress riser,” in a hollow cylinder under torsional
load results in a three- to fourfold increase in local stress concentration. Creating a slit along the entire length of a hollow cylinder creates an “open section” that is free to warp under torsional load. The weakening effect is catastrophic, with a “closed section” being 400 times stiffer and 30 times stronger than an “open section.” To avoid the dramatic strength reduction caused by this “open-section’’ effect, it has been variously recommended in the clinical literature that cortical defects be kept to less than one-third, one-half, or the full diameter of the bone (1,13,14). Yet, experimental confirmation of these clinical “rules of thumb” is lacking in the literature. No study has evaluated a broad range of cortical defects under torsional load to determine their mechanical effect. By initiating a systematic investigation of this question, the authors have developed a reproducible tor-
Received September 11, 1989; accepted April 26, 1990. Address correspondence and reprint requests to Dr. B. F. Morrey at Department of Orthopaedics, Mayo Clinic/Mayo Foundation, Rochester, Minnesota 55905, U.S.A.
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B . C . EDGERTON ET AL.
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sional testing technique for long bones (9). The second phase of this investigation is reported here. The purpose of this study was to test a broad range of circular defects under torsional load to identify the smallest defect resulting in strength reduction-the stress riser-as well as the defect size, if any, leading to the marked strength reduction, i.e., the opensection dimension. MATERIALS AND METHODS
Fresh-frozen sheep femora had been previously identified by studying 50 pairs as a physically uniform test population (9). Using the described technique of mounting and torsional testing, there is no statistically significant difference in strength between the two bones of a pair. The posterior cortex was identified as the most sensitive to small defects. In this study, the specimens were procured, stored, and mounted by the method previously described, with the defects placed in the posterior cortex. This method was demonstrated to be reliable and reproducible for showing torsional load strength in the intact and defect bone. Experimental Design
Thirty-five pairs of femora were tested in torsion to failure with posterior unicortical defects ranging from 10 to 60% of mediolateral bone diameter. One bone of each pair contained the defect while the opposite bone was left intact. Torsional strength reduction was then correlated with defect size. Measurements
Anteroposterior and lateral radiographs were made of the bone pairs to measure bone length, bone diameter (anteroposterior and mediolateral), medullary canal diameter, and the thickness of each cortex. The square mounts on each end of the bone laid flat on the radiographic plate, assuring identical radiographic projection of all specimens. Production of Defects
The square metal mounts on the ends of each specimen were used to hold the specimen firmly in the vise of a Bridgeport Vertical Milling Machine (Bridgeport, CT, U.S.A.). Using the digital x-y coordinate readout, the location of the defect in the
J Orthop Res, Vol. 8,No. 6 , 1990
middiaphyseal posterior cortex was controlled to within 100 pm. Each defect was created by drilling with progressively larger metric drill bits at 660 rpm to avoid splintering at the edges of the defect. The identical rotational alignment of each specimen within the metal mounts insured that the defects would be placed in the same location in each specimen. A 60% cortical defect is equal to the medullary canal diameter. Because larger defects would notch the medial and lateral cortices, the 60% defect was the largest tested. Torsional Testing
All specimens were tested on a uniaxial MTS machine (Minneapolis, MN, U.S.A.) in internal torsion to failure at a rapid rate (30” per second) and zero axial load. The results of torque (N cm) vs. angular deformation (in degrees) were plotted for graphical interpretation. By integrating the area under the torque-displacement curve, the energy absorption to failure was obtained (N cm). The initial stiffness of the bones was also calculated directly from the slope of the curve, and the influence of defects on stiffness values was studied. The bone samples were kept moist with saline-soaked sponges throughout the mounting, machining, and testing protocols. The percentage of the original torsional strength remaining in a bone with a defect compared to its intact control was calculated for each of the parameters: torque, energy, and rotation. By statistical analysis of variance, the smallest defect causing a decrease in strength with a p value of
Torsional Strength Reduction Due to Cortical Defects in Bone Bradley C. Edgerton, Kai-Nan An, and Bernard F. Morrey Biomechanics Laboratory, Department of Orthopaedics, Mayo CliniclMayo Foundation, Rochester, Minnesota, U.S.A.
Summary: This study correlated torsional strength reduction with circular defect size in cortical bone, to define the “stress riser” and “open-section’’ effect of the defects. The experimental model was developed and verified. Circular defects from 10 to 60% of bone diameter were then created in paired sheep femora and the bones loaded to failure. Contrary to theory, this experimental study suggests that small defects (10%) of bone diameter cause no significant torsional strength reduction. A 20% defect caused a 34% decrease in strength, representing the “stress riser” dimension. Defects between 20 and 60% of bone diameter decreased strength linearly as a function of defect size, and thus no discrete “open section” dimension was identified. For circular defects, we were unable to demonstrate a discrete “open-section’’ effect at which dramatic strength reduction is observed. These data may prove to be helpful when planning surgery that involves placing defects in bone such as for infection, biopsy, and prosthesis removal. The accepted guideline to avoid defects of greater than 50% of the bone diameter may be too great. Our data reveal this 62% reduction in torque strength and 88% energy to failure exist with a 50% circular defect. Key Words: Cortical bone-Torsional strengthCircular defect.
The complications occurring because of cortical defects in bone are well recognized in the clinical practice of orthopaedics. Whether due to biopsy, tumor, or internal fixation, these defects frequently lead to pathologic fracture (6,7,10,16,19). In contrast to their clinical relevance, little experimental data exist correlating defect size with strength reduction in cortical bone. The engineering literature, however, does provide detailed information about material irregularities, and two classes of defects have been described (15,17,20,22). A hole of infinitely small size, a “stress riser,” in a hollow cylinder under torsional
load results in a three- to fourfold increase in local stress concentration. Creating a slit along the entire length of a hollow cylinder creates an “open section” that is free to warp under torsional load. The weakening effect is catastrophic, with a “closed section” being 400 times stiffer and 30 times stronger than an “open section.” To avoid the dramatic strength reduction caused by this “open-section’’ effect, it has been variously recommended in the clinical literature that cortical defects be kept to less than one-third, one-half, or the full diameter of the bone (1,13,14). Yet, experimental confirmation of these clinical “rules of thumb” is lacking in the literature. No study has evaluated a broad range of cortical defects under torsional load to determine their mechanical effect. By initiating a systematic investigation of this question, the authors have developed a reproducible tor-
Received September 11, 1989; accepted April 26, 1990. Address correspondence and reprint requests to Dr. B. F. Morrey at Department of Orthopaedics, Mayo Clinic/Mayo Foundation, Rochester, Minnesota 55905, U.S.A.
851
B . C . EDGERTON ET AL.
852
sional testing technique for long bones (9). The second phase of this investigation is reported here. The purpose of this study was to test a broad range of circular defects under torsional load to identify the smallest defect resulting in strength reduction-the stress riser-as well as the defect size, if any, leading to the marked strength reduction, i.e., the opensection dimension. MATERIALS AND METHODS
Fresh-frozen sheep femora had been previously identified by studying 50 pairs as a physically uniform test population (9). Using the described technique of mounting and torsional testing, there is no statistically significant difference in strength between the two bones of a pair. The posterior cortex was identified as the most sensitive to small defects. In this study, the specimens were procured, stored, and mounted by the method previously described, with the defects placed in the posterior cortex. This method was demonstrated to be reliable and reproducible for showing torsional load strength in the intact and defect bone. Experimental Design
Thirty-five pairs of femora were tested in torsion to failure with posterior unicortical defects ranging from 10 to 60% of mediolateral bone diameter. One bone of each pair contained the defect while the opposite bone was left intact. Torsional strength reduction was then correlated with defect size. Measurements
Anteroposterior and lateral radiographs were made of the bone pairs to measure bone length, bone diameter (anteroposterior and mediolateral), medullary canal diameter, and the thickness of each cortex. The square mounts on each end of the bone laid flat on the radiographic plate, assuring identical radiographic projection of all specimens. Production of Defects
The square metal mounts on the ends of each specimen were used to hold the specimen firmly in the vise of a Bridgeport Vertical Milling Machine (Bridgeport, CT, U.S.A.). Using the digital x-y coordinate readout, the location of the defect in the
J Orthop Res, Vol. 8,No. 6 , 1990
middiaphyseal posterior cortex was controlled to within 100 pm. Each defect was created by drilling with progressively larger metric drill bits at 660 rpm to avoid splintering at the edges of the defect. The identical rotational alignment of each specimen within the metal mounts insured that the defects would be placed in the same location in each specimen. A 60% cortical defect is equal to the medullary canal diameter. Because larger defects would notch the medial and lateral cortices, the 60% defect was the largest tested. Torsional Testing
All specimens were tested on a uniaxial MTS machine (Minneapolis, MN, U.S.A.) in internal torsion to failure at a rapid rate (30” per second) and zero axial load. The results of torque (N cm) vs. angular deformation (in degrees) were plotted for graphical interpretation. By integrating the area under the torque-displacement curve, the energy absorption to failure was obtained (N cm). The initial stiffness of the bones was also calculated directly from the slope of the curve, and the influence of defects on stiffness values was studied. The bone samples were kept moist with saline-soaked sponges throughout the mounting, machining, and testing protocols. The percentage of the original torsional strength remaining in a bone with a defect compared to its intact control was calculated for each of the parameters: torque, energy, and rotation. By statistical analysis of variance, the smallest defect causing a decrease in strength with a p value of
