Journal of Orthopaedic Research 8:843650 Raven Press, Ltd., New York 0 1990 Orthopaedic Research Society
A Study of Fracture Callus Material Properties: Relationship to the Torsional Strength of Bone Mark D. Markel, Mark A. Wikenheiser, and Edmund Y. S. Chao Biomechanics Laboratory, Department of Orthopedics, Mayo CliniclMayo Foundation, Rochester, Minnesota, U.S.A.
Summary: This study was designed to quantitate the local material properties of fracture callus during gap healing and to relate these local properties to the torsional strength of bone in a canine model under external fixation. Bilateral tibia1 transverse osteotomies were performed in 32 dogs and stabilized using unilateral external skeletal fixators with a 2-mm gap. Dogs were divided into four equal groups and euthanized at either 2, 4, 8, or 12 weeks. The torsional properties of one bone of each pair were determined. In both bones of each pair, the indentation stiffness, calcium content, and histomorphometric properties of six sites of periosteal callus, six sites of endosteal callus, four sites of cortical bone, and two sites of gap tissue were determined. Each of the four types of tissue had a specific structural or material property change during the study period. The indentation stiffness of penosteal callus increased up to 8 weeks and then plateaued. Endosteal callus stiffness peaked at 8 weeks and then decreased by 12 weeks. Gap tissue stiffness increased linearly over time. Cortical bone stiffness decreased over time. Indentation stiffness was significantly associated with the calcium content of periosteal callus (R2 = 0.50, p < 0.0001) and gap tissue (R2 = 0.66, p < 0.OOOl). The local stiffnesses of gap tissue and periosteal callus were significantly associated with the maximum torque (gap, R2 = 0.50, p < 0.0001; periosteal, R2 = 0.34, p < 0.05) and the torsional stiffness (gap, R2 = 0.44, p < 0.0001; periosteal, R2 = 0.65, p < 0.0001) of the bone. Changes in local material properties corresponded to histologic changes in new bone formation and porosity of the four tissues. Key Words: Fracture healing-Callus material properties-Indentation testing.
The justification for noninvasive evaluation of local regions of bone is the relationship between local material and structural properties with the structural strength of bone (8,18,19). Although many studies have reported the association between bone strength and bone mineral density (9,10,19), few
have examined healing fractures and the association between callus material properties and the bone’s torsional strength (5). Studies examining the material properties of healing bones will further our understanding of the association between calcium content, local stiffness, and the structural strength of bone and possibly allow better prediction of bone material properties. This study was designed to determine the association between the local material and structural properties of healing bone and the bone’s torsional
Received December 14, 1989; accepted April 10, 1990. Address correspondence and reprint requests to Dr. E. Y. S. Chao at Orthopedic Biomechanics Lab, Mayo Clinic, Rochester, MN 55905, U.S.A.
843
844
M . D . MARKEL ET A L .
strength. These associations were examined in a canine secondary gap healing model under stable external fixation. MATERIALS AND METHODS Thirty-two adult mixed breed dogs were used for this experiment. The dogs were divided into four equal groups of eight dogs that were euthanized at one of the following four time periods after surgery; 2 , 4 , 8 , or 12 weeks. Dogs are an accepted model for evaluating bone healing (16,23). Maturity was confirmed by radiographic examination of the proximal tibia1 and distal femoral physes. Closed and obliterated physes were considered as mature. Large dogs of similar size were used for the experiment (mean weight of 23.6 kg; range of 16.8-33.6 kg). Identical surgical procedures were performed on both hind limbs of each dog. Dogs were anesthetized with sodium pentobarbital (25 mg/kg, i.v.), placed in dorsal recumbency, and aseptically prepared and draped for surgery. A 5-cm skin incision extending through the periosteum was made over the medial diaphysis of the tibia. The periosteum was bluntly elevated over the circumference of the proposed osteotomy site. A middiaphyseal transverse osteotomy was made with an oscillating saw (Model 1370, Stryker Corp., Kalamazoo, MI, U.S.A.). The osteotomy location was standardized using radiographic control by accounting for magnification and then measuring proximally from the lateral malleolus. The osteotomy was stabilized (2mm gap) using a small Orthofix unilateral external fixator (EBI Medical Systems, Inc., Fairfield, NJ, U.S.A.). The gap was standardized with a 2-mm thick aluminum spacer. The incision was closed in three layers in routine fashion. Dogs were allowed to ambulate freely during the study period. New bone formation was quantitated with continuous tetracycline (500 mg, P.o., once daily) labeling starting the day of surgery. This is less than the dose of 60 mg/kg that inhibits bone formation (12). Craniocaudal and mediolateral radiographs were taken immediately after surgery to evaluate osteotomy reduction and pin placement and then biweekly until euthanasia. The amount of radiographic periosteal callus formation was determined using a sonic digitizer. Periosteal callus formation was evaluated at the medial, lateral, cranial, and caudal cortices centered over the middle 3.0 cm of bone and expressed in units of area (mm2). After determining the callus area, it was normalized by
J Orthop Res, Vol. 8, N o . 6 , 1990
dividing the amount of callus at each cortex by the total area of tibia (cortex and medullary cavity) centered over the middle 3.0 cm of bone. This region of bone was selected because it was the largest region that could be measured without incorporating periosteal new bone associated with the pins nearest the osteotomy in the analysis. All tibiae were cut into segments 11.4 cm long and mounted in Wood's metal (Cerro-Bend alloy, Satterlee Co., Minneapolis, MN, U.S.A.) heated above its melting point of 70°C (24). Axial torsion with external rotation at a low strain rate (15"/min) was applied to one randomly selected tibia of each dog on an Instron Electro-mechanical Testing Machine (Model 1125, Instron Corp., Canton, MA, U.S.A.) until bone failure occurred. A low rate of loading was chosen to minimize inertial effects that may be present at fast loading rates (7,25). Maximum torque and torsional stiffness were determined from the torque angular displacement curve. These data provide the structural properties of bone at different stages of osteotomy healing. A 2-mm thick coronal section of each tibia centered over the osteotomy site was cut for indentation testing and mineral content determination using a high concentration diamond wafering blade. Both of the remaining halves of bone were fixed in 70% alcohol within 5 h of euthanasia for histomorphometric and microradiographic analyses. Indentation testing of 18 specific regions was performed using an Instron Biaxial Testing Machine (Model 1321, Instron Corp.). Sites were tested using a 1.5-mm diameter indentor with a spherical testing surface of 1.5 mm diameter. These regions incorporated six sites of periosteal callus, six sites of endosteal callus, four sites of cortical bone, and two sites of gap tissue (Fig. 1). The diameter of the indentor was 1.5 mm so that gap tissue (2-mm gap) and cortex (-3-mm width) could be readily tested. The coronal sections were mounted on a rigid stage, and indentation was performed normal to the cut surface at a constant displacement rate of 2.75 mm/min to a fixed depth of 0.375 mm. A low loading rate was used to obtain a static response. The depth of indentation (0.375 mm) was to insure loading to just beyond the yield point (Fig. 2). The slope of the linear portion of the curve, which is an index of the foundation stiffness of the bone, was measured. The 18 regions of interest within the 2.0 mm x 30 mm unembedded coronal section of each tibia were analyzed for mineral content after indentation testing. A 1.5-mm diameter trephine was used to sam-
FRACTURE CALLUS RELATION TO TORSIONAL STRENGTH 2.0 mm
Med. 1
cm
lcm
Perrosteal callus
FIG. 1. Illustration of 18 regions of osteotomy in which indentation stiffness, mineral content, new bone formation, and porosity were determined. (Reprinted with permission of the Mayo Foundation.)
ple the exact site used for indentation testing. The samples were weighed, dried in a 100°C oven for 48 h, and then were dissolved in concentrated HNO, for 48 h. The mineral content of the resultant solution was determined by an inductively coupled plasma atomic emission spectroscopy technique (20). Data were calculated as mg of Ca2+/g of dry weight of tissue. The bone halves remaining after removal of the 2-mm coronal section were fixed in 70% alcohol and dehydrated in increasing concentrations of alcohol
25
r
20
z d (D
0 A 10
5
0 0
0.1
0.2
0.3
0.4
Displacement, mm FIG. 2. Typical (4-week gap tissue) load-deformation curve demonstrating the linear portion of curve from which indentation stiffness is calculated.
845
(6). After dehydration was complete, the specimens were defatted using xylene and embedded in methylmethacrylate. The blocks then were cut to an undecalcified bone section width of 200 pm using a low-speed diamond saw, and the specimens were ground to the desired thickness of 98-100 pm between two pieces of plate glass roughened with #120 grit carborundum. Only one section immediately adjacent to the section taken for indentation testing was prepared. Microradiographs of the coronal section were made using high-resolution contact film (Kodak spectroscopic plates, Eastman Kodak, Rochester, NY, U.S.A.) according to methods previously described (15). Bone porosity was quantitated with a semiautomated computerized image analyzer, including a video image processor (Datacube, Inc., Peabody, MA, U.S.A.) with a microscope and custom-made software. The porosity of periosteal and endosteal callus and gap tissue was expressed as a percentage of the total new bone labeled by tetracycline. The intracortical porosity was expressed as a percentage of the total bone in the regions analyzed. This method has been verified in previous studies in our laboratory (4,16). Porosity was measured for each area of the 18 specific sites. The rate of new bone formation was studied using a previously described tetracycline labeling technique using point counting (11,28). The amounts of the new bone, porosity, and unlabeled cortical bone were expressed as a percent of each region of interest. Therefore, at each specific cortical site, new bone formation, original unlabeled bone, and porosity were measured. In the gap tissue and callus sites, there was no original bone, so only new bone formation and porosity were calculated. The mean value for the six sites of periosteal callus, the six sites of endosteal callus, the four sites of cortex, and the two sites of gap tissue were determined for each tibia for indentation stiffness, calcium content, new bone formation, and porosity. Paired comparisons using a Student’s t test between the right and left limb were performed for each of these four types of tissue. Since there were no differences between the right and left tibiae, the results of the two limbs were averaged. Torsional stiffness, maximum torque, and callus quantity were analyzed separately for the effect of time (2, 4, 8, and 12 weeks) on these parameters. These comparisons were performed with one-way analysis of variance (ANOVA) and were followed
J
Orthop Res, Vol. 8, NO. 6, 1990
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M . D . MARKEL ET A L .
by Tukey's studentized range post hoc t test when ANOVA revealed significant differences. In addition, the mean values for indentation stiffness, calcium content, new bone formation, and porosity for each type of tissue (periosteal, endosteal, cortex, and gap) were analyzed separately for the effect of time on these parameters with ANOVA and were followed by Tukey's studentized range post hoc t test when ANOVA revealed significant differences. The association between the mean values of indentation stiffness, calcium content, radiographically determined callus quantity, maximum torque, and torsional stiffness were quantitated with leastsquares regression. Data were correlated for each specific tissue (periosteal, endosteal, gap, or cortex) with 32 independent points (one for each dog) per correlation. Stepwise regression was also performed between the independent variables (calcium content, indentation stiffness, and callus quantity) and the dependent variables (maximum torque and torsional stiffness). The independent and dependent variables were chosen a priori to determine the association between local material properties and volume of callus and the structural properties of healing bone. All differences and associations were considered to be significant at a probability level of 95% (p < 0.05). All statistical analyses were performed with a
commercially available software program (SAS Institute, Inc., Cary, NC, U.S.A.).
RESULTS The local indentation stiffness of gap tissue increased linearly over time (Table 1). In periosteal tissue, stiffness increased up to 8 weeks and then plateaued at 12 weeks. Endosteal stiffness peaked at 8 weeks and then decreased by 12 weeks. Cortical stiffness decreased over time. The calcium content of gap tissue and periosteal callus increased over time (Table 1). The regression equations to describe dry weight of calcium change over time are linear for periosteal, endosteal, and gap tissue. There were no significant changes in cortical calcium content over time (Table 1). The percent unlabeled cortical bone decreased as a log function over time. New bone formation peaked in periosteal and endosteal callus at 4 weeks and then plateaued (periosteal) or declined (endosteal) by 12 weeks (Table 1). In gap tissue and cortical bone, new bone formation increased over time. Porosity decreased and plateaued in periostea1 callus, whereas endosteal callus porosity increased to greater than 2-week values by 12 weeks (Table 1). The porosity of gap tissue decreased with time but plateaued between 8 and 12 weeks.
TABLE 1. Local properties of healing osteotomy Weeks after surgery
Periosteal Mean
2 4 8 12
38.3" 48.6" 197.6' 138.2'
2 4 8 12
170.3" 155.8" 23 1.5' 255.3'
2 4 8 12
39.9" 63.4' 58.5' 59.6'
2 4 8 12
60.1" 36.4' 41.5' 40.4'
Gap SEM
Mean
Endosteal SEM
Mean
Cortex SEM
Indentation stiffness, region of interest stiffness (N/mm) 11.1 6.0 12.7" 31.3" 6.7 7.5 18.5" 6.0 48.3" 10.6 14.3 90.9' 21.4 98.9' 29.7 23.9 26.0 153.7' 40.2" 8.2 Calcium content (per dry weight), region of interest calcuim content (mg of calciumig of dry weight) 19.4 88.9" 31.9 178.8",b 13.2 10.3 86.5" 23.5 165.8" 16.2 6.0 229.5' 14.5 8.8 220. 2',' 13.4 232.0' 7.9 231.6' 23.5 Microradiographic new bone formation, region of interest new bone (%) 5.9 0.4" 0.4 25.0" 3.9 2.4 23.2' 7.3 42.4' 3.6 2.2 58.1' 3.1 35.2' 2.3 2.5 62.0" 1.6 13.0' 2.9 Porosity of bone regions, region of interest porosity (%) 5.9 99.6" 0.4 75.0" 3.9 2.4 76.8' 7.3 57.7' 3.6 2.2 41.9' 3.1 64.8' 2.3 2.5 38.0' 1.6 87.0' 2.9
Mean 892.7" 720.0". 589.5' 655.8'
SEM
'
261.3" 249.3" 255.0" 243.1"
8.5 11.1 2.5 7.3
3.2" 9.6" 20.2' 38.5"
0.8 1.5 1.8 2.0
11.5" 22.3' 21.3' 16.7'
1.o 1.2 3.8 2.1
Within a column for each parameter, superscripts of differing letters are significantly different from each other (p < 0.05). SEM = standard error of the mean.
J Orthop Res, Vol. 8, No. 6 , 1990
68.0 76.1 50.0 38.0
FRACTURE CALLUS RELATION TO TORSIONAL STRENGTH The 2-week osteotomies deformed in torsion but did not fracture, so the maximum torque could not be determined (Table 2). The maximum torque and torsional stiffness of the osteotomies increased over time and were significantly less strong than intact bone specimens at 12 weeks (Table 2). Radiographic callus formation peaked at 6 weeks and then gradually decreased (Table 3). At all time intervals, the lateral callus was greater than the medial, cranial, or caudal callus. In contrast, the medial callus was the smallest compared to the other three locations. The association between indentation stiffness and calcium content was moderately high (R2 = 0.66 and 0.50, p < 0.0001) for gap tissue and periosteal callus, respectively. The association between indentation stiffness of gap tissue and periosteal callus to the torsional strength of bone revealed moderate correlations with maximum torque (gap, R2 = 0.50, p < 0.0001 (Fig. 3, left); periosteal, R2 = 0.34, p < 0.05) and torsional stiffness (gap, R2 = 0.44, p < 0.0001; periosteal, R2 = 0.65, p < 0.0001). The association between the calcium content of the periosteal callus, endosteal callus, and gap tissue to torsional properties also revealed moderate correlations with the maximum torque (periosteal, R2 = 0.37, p < 0.05; endosteal, R2 = 0.31, p < 0.05; gap, R2 = 0.44, p < 0.005), and torsional stiffness (periosteal, R2 = 0.50, p < 0.0001; endosteal, R2 = 0.43, p < 0.0005; gap, R2 = 0.48, p < 0.0001 (Fig. 3, right)). Stepwise regression of the calcium content and indentation stiffness of gap tissue and periosteal callus to the maximum torque revealed that only indentation stiffness (gap, R2 = 0.50; p < 0.0001; periosteal, R2 = 0.34, p < 0.05) contributed signifTABLE 2. Torsional properties of healing osteotomy Torsional Values ~~~
Weeks after surgery Intact bone 2 4
8 12
Ultimate torque (Nm)
Torsional stiffness (Nm/rad)
Mean
SEM
Mean
SEM
28.5" NA 3.6* 15.6" 12.2'
2.3 NA 0.7 2.1 1.5
163.6" 0.9b 22.3'*'
15.3 0.2 9.8 10.5 7.6
77Sd 54.gd
SEM = standard error of the mean. NA = not applicable. Torsional properties weeks after surgery. Within a column, superscripts of differing letters are significantly different from each other (p < 0.05).
84 7
icantly to the regression when both parameters were in the model. In contrast, stepwise regression of the calcium content and indentation stiffness to the torsional stiffness of the bone revealed that calcium content alone contributed to the correlation coefficient in gap tissue (R2 = 0.44, p < O.OOOl), and local stiffness alone contributed significantly to the correlation coefficient in periosteal callus (R2 = 0.65, p < 0.0001). When calcium content, indentation stiffness, and radiographically determined callus quantity were included in stepwise regression, the callus quantity always contributed to the association between these parameters and torsional stiffness and the maximum torque of the bone. The callus quantity (gap, R2 = 0.21, p < 0.05; periosteal, R2 = 0.31, p < 0.05) with (gap, R2 = 0.33, p < 0.01) or without (periosteal, p > 0.05) indentation stiffness and without calcium content significantly contributed to the correlation coefficient with maximum torque (gap, R2 = 0.54, p < 0.005; periosteal, R2 = 0.31, p < 0.05). In contrast, calcium content (gap, R2 = 0.40, p < 0.001; periosteal callus, R2 = 0.12, p < 0.01) and callus quantity (gap, R2 = 0.21, p < 0.0001; periosteal, R2 = 0.53, p < 0.001) but not indentation stiffness significantly contributed to the model with torsional stiffness (gap, R2 = 0.61; p < 0.005; periosteal, R2 = 0.65, p < 0.0001). DISCUSSION Indentation testing as a means of determining compressive resistance (indentation stiffness) is a relatively simple and quick method. In contrast, most studies machine bone into various shapes to determine Young's modulus (10,13). The machining process is tedious and slow, thereby minimizing the number of sites that can be tested. Indentation testing requires only a surface to be tested and can readily be used in as many areas as is required for the study. Indentation testing has been used for determining the stiffness of the distal tibia (l), the proximal tibia (13), the patella (14), and periosteal callus in rats (5). Indentation with a consistent geometry resulted in similar-shaped load-deformation curves and is therefore an appropriate measure of local material stiffness. The changes in calcium content observed in the tibia1 osteotomies of this study are consistent with previous studies of rat fractures (2,5) and dog osteotomies (22). The gap tissue calcium content increased with time, by l 2 weeks it had not reached cortical values for calcium content. The
J Orthop Res, Vol. 8, No. 6 , 1990
M . D . MARKEL ET A L . TABLE 3. Radiographic callus formation Normalized radiographic callus, callus location Medial
Lateral
Anterior
Posterior
Weeks after surgery
Mean
SEM
Mean
SEM
Mean
SEM
Mean
SEM
2" 4 6 8 10 12
0.002",* 0.033",* 0.060", * 0.059". * 0.036"** 0.024",*
0.001 0.007 0.012 0.015 0.018 0.015
0.03",** 0.15',** 0.29c.** 0.26',** 0.22",** 0.15',**
0.007 0.024 0.041 0.021 0.032 0.035
0.02"'.** 0.09'*** 0.17",*** 0. 14c8*** 0.09',* 0.08',***
0.007 0.016 0.033 0.022 0.025 0.025
0.03"*** 0.1 Ia.b.** 0.20=3*** 0.18b,C,*** O.ll",b,* 0.08"****
0.012 0.022 0.034 0.028 0.035 0.036
SEM = standard error of the mean. Within a row, superscripts of differing number of asterisks are significantly different from each other (p < 0.05). Within a column, superscripts of differing letters are significantly different from each other (p < 0.05). Radiographic callus was normalized to the area of tibia at the region analyzed.
gap tissue calcium content would not be expected to reach cortical levels until the gap both had completely filled with new bone and also had completely remodeled (26). This remodeling may take from 1-3 years and was only just beginning by 12 weeks when the longest time group in this study was euthanized. The periosteal callus calcium content increased during the study but had plateaued by 12 weeks. This would be expected because periosteal callus is initially formed to anchor the bone ends and bridge the osteotomy. As the bone becomes stable, periosteal callus is resorbed by osteoclasts, therefore negating the need for progressive mineralization of the periosteal callus. Additionally, porosity of the periosteal callus initially decreased, which would be expected to be associated with increased calcium content, but then gradually increased as the callus was resorbed, probably minimizing any further increases in periosteal callus calcium content.
y=-5.69
+ 9.36 log x
p
A Study of Fracture Callus Material Properties: Relationship to the Torsional Strength of Bone Mark D. Markel, Mark A. Wikenheiser, and Edmund Y. S. Chao Biomechanics Laboratory, Department of Orthopedics, Mayo CliniclMayo Foundation, Rochester, Minnesota, U.S.A.
Summary: This study was designed to quantitate the local material properties of fracture callus during gap healing and to relate these local properties to the torsional strength of bone in a canine model under external fixation. Bilateral tibia1 transverse osteotomies were performed in 32 dogs and stabilized using unilateral external skeletal fixators with a 2-mm gap. Dogs were divided into four equal groups and euthanized at either 2, 4, 8, or 12 weeks. The torsional properties of one bone of each pair were determined. In both bones of each pair, the indentation stiffness, calcium content, and histomorphometric properties of six sites of periosteal callus, six sites of endosteal callus, four sites of cortical bone, and two sites of gap tissue were determined. Each of the four types of tissue had a specific structural or material property change during the study period. The indentation stiffness of penosteal callus increased up to 8 weeks and then plateaued. Endosteal callus stiffness peaked at 8 weeks and then decreased by 12 weeks. Gap tissue stiffness increased linearly over time. Cortical bone stiffness decreased over time. Indentation stiffness was significantly associated with the calcium content of periosteal callus (R2 = 0.50, p < 0.0001) and gap tissue (R2 = 0.66, p < 0.OOOl). The local stiffnesses of gap tissue and periosteal callus were significantly associated with the maximum torque (gap, R2 = 0.50, p < 0.0001; periosteal, R2 = 0.34, p < 0.05) and the torsional stiffness (gap, R2 = 0.44, p < 0.0001; periosteal, R2 = 0.65, p < 0.0001) of the bone. Changes in local material properties corresponded to histologic changes in new bone formation and porosity of the four tissues. Key Words: Fracture healing-Callus material properties-Indentation testing.
The justification for noninvasive evaluation of local regions of bone is the relationship between local material and structural properties with the structural strength of bone (8,18,19). Although many studies have reported the association between bone strength and bone mineral density (9,10,19), few
have examined healing fractures and the association between callus material properties and the bone’s torsional strength (5). Studies examining the material properties of healing bones will further our understanding of the association between calcium content, local stiffness, and the structural strength of bone and possibly allow better prediction of bone material properties. This study was designed to determine the association between the local material and structural properties of healing bone and the bone’s torsional
Received December 14, 1989; accepted April 10, 1990. Address correspondence and reprint requests to Dr. E. Y. S. Chao at Orthopedic Biomechanics Lab, Mayo Clinic, Rochester, MN 55905, U.S.A.
843
844
M . D . MARKEL ET A L .
strength. These associations were examined in a canine secondary gap healing model under stable external fixation. MATERIALS AND METHODS Thirty-two adult mixed breed dogs were used for this experiment. The dogs were divided into four equal groups of eight dogs that were euthanized at one of the following four time periods after surgery; 2 , 4 , 8 , or 12 weeks. Dogs are an accepted model for evaluating bone healing (16,23). Maturity was confirmed by radiographic examination of the proximal tibia1 and distal femoral physes. Closed and obliterated physes were considered as mature. Large dogs of similar size were used for the experiment (mean weight of 23.6 kg; range of 16.8-33.6 kg). Identical surgical procedures were performed on both hind limbs of each dog. Dogs were anesthetized with sodium pentobarbital (25 mg/kg, i.v.), placed in dorsal recumbency, and aseptically prepared and draped for surgery. A 5-cm skin incision extending through the periosteum was made over the medial diaphysis of the tibia. The periosteum was bluntly elevated over the circumference of the proposed osteotomy site. A middiaphyseal transverse osteotomy was made with an oscillating saw (Model 1370, Stryker Corp., Kalamazoo, MI, U.S.A.). The osteotomy location was standardized using radiographic control by accounting for magnification and then measuring proximally from the lateral malleolus. The osteotomy was stabilized (2mm gap) using a small Orthofix unilateral external fixator (EBI Medical Systems, Inc., Fairfield, NJ, U.S.A.). The gap was standardized with a 2-mm thick aluminum spacer. The incision was closed in three layers in routine fashion. Dogs were allowed to ambulate freely during the study period. New bone formation was quantitated with continuous tetracycline (500 mg, P.o., once daily) labeling starting the day of surgery. This is less than the dose of 60 mg/kg that inhibits bone formation (12). Craniocaudal and mediolateral radiographs were taken immediately after surgery to evaluate osteotomy reduction and pin placement and then biweekly until euthanasia. The amount of radiographic periosteal callus formation was determined using a sonic digitizer. Periosteal callus formation was evaluated at the medial, lateral, cranial, and caudal cortices centered over the middle 3.0 cm of bone and expressed in units of area (mm2). After determining the callus area, it was normalized by
J Orthop Res, Vol. 8, N o . 6 , 1990
dividing the amount of callus at each cortex by the total area of tibia (cortex and medullary cavity) centered over the middle 3.0 cm of bone. This region of bone was selected because it was the largest region that could be measured without incorporating periosteal new bone associated with the pins nearest the osteotomy in the analysis. All tibiae were cut into segments 11.4 cm long and mounted in Wood's metal (Cerro-Bend alloy, Satterlee Co., Minneapolis, MN, U.S.A.) heated above its melting point of 70°C (24). Axial torsion with external rotation at a low strain rate (15"/min) was applied to one randomly selected tibia of each dog on an Instron Electro-mechanical Testing Machine (Model 1125, Instron Corp., Canton, MA, U.S.A.) until bone failure occurred. A low rate of loading was chosen to minimize inertial effects that may be present at fast loading rates (7,25). Maximum torque and torsional stiffness were determined from the torque angular displacement curve. These data provide the structural properties of bone at different stages of osteotomy healing. A 2-mm thick coronal section of each tibia centered over the osteotomy site was cut for indentation testing and mineral content determination using a high concentration diamond wafering blade. Both of the remaining halves of bone were fixed in 70% alcohol within 5 h of euthanasia for histomorphometric and microradiographic analyses. Indentation testing of 18 specific regions was performed using an Instron Biaxial Testing Machine (Model 1321, Instron Corp.). Sites were tested using a 1.5-mm diameter indentor with a spherical testing surface of 1.5 mm diameter. These regions incorporated six sites of periosteal callus, six sites of endosteal callus, four sites of cortical bone, and two sites of gap tissue (Fig. 1). The diameter of the indentor was 1.5 mm so that gap tissue (2-mm gap) and cortex (-3-mm width) could be readily tested. The coronal sections were mounted on a rigid stage, and indentation was performed normal to the cut surface at a constant displacement rate of 2.75 mm/min to a fixed depth of 0.375 mm. A low loading rate was used to obtain a static response. The depth of indentation (0.375 mm) was to insure loading to just beyond the yield point (Fig. 2). The slope of the linear portion of the curve, which is an index of the foundation stiffness of the bone, was measured. The 18 regions of interest within the 2.0 mm x 30 mm unembedded coronal section of each tibia were analyzed for mineral content after indentation testing. A 1.5-mm diameter trephine was used to sam-
FRACTURE CALLUS RELATION TO TORSIONAL STRENGTH 2.0 mm
Med. 1
cm
lcm
Perrosteal callus
FIG. 1. Illustration of 18 regions of osteotomy in which indentation stiffness, mineral content, new bone formation, and porosity were determined. (Reprinted with permission of the Mayo Foundation.)
ple the exact site used for indentation testing. The samples were weighed, dried in a 100°C oven for 48 h, and then were dissolved in concentrated HNO, for 48 h. The mineral content of the resultant solution was determined by an inductively coupled plasma atomic emission spectroscopy technique (20). Data were calculated as mg of Ca2+/g of dry weight of tissue. The bone halves remaining after removal of the 2-mm coronal section were fixed in 70% alcohol and dehydrated in increasing concentrations of alcohol
25
r
20
z d (D
0 A 10
5
0 0
0.1
0.2
0.3
0.4
Displacement, mm FIG. 2. Typical (4-week gap tissue) load-deformation curve demonstrating the linear portion of curve from which indentation stiffness is calculated.
845
(6). After dehydration was complete, the specimens were defatted using xylene and embedded in methylmethacrylate. The blocks then were cut to an undecalcified bone section width of 200 pm using a low-speed diamond saw, and the specimens were ground to the desired thickness of 98-100 pm between two pieces of plate glass roughened with #120 grit carborundum. Only one section immediately adjacent to the section taken for indentation testing was prepared. Microradiographs of the coronal section were made using high-resolution contact film (Kodak spectroscopic plates, Eastman Kodak, Rochester, NY, U.S.A.) according to methods previously described (15). Bone porosity was quantitated with a semiautomated computerized image analyzer, including a video image processor (Datacube, Inc., Peabody, MA, U.S.A.) with a microscope and custom-made software. The porosity of periosteal and endosteal callus and gap tissue was expressed as a percentage of the total new bone labeled by tetracycline. The intracortical porosity was expressed as a percentage of the total bone in the regions analyzed. This method has been verified in previous studies in our laboratory (4,16). Porosity was measured for each area of the 18 specific sites. The rate of new bone formation was studied using a previously described tetracycline labeling technique using point counting (11,28). The amounts of the new bone, porosity, and unlabeled cortical bone were expressed as a percent of each region of interest. Therefore, at each specific cortical site, new bone formation, original unlabeled bone, and porosity were measured. In the gap tissue and callus sites, there was no original bone, so only new bone formation and porosity were calculated. The mean value for the six sites of periosteal callus, the six sites of endosteal callus, the four sites of cortex, and the two sites of gap tissue were determined for each tibia for indentation stiffness, calcium content, new bone formation, and porosity. Paired comparisons using a Student’s t test between the right and left limb were performed for each of these four types of tissue. Since there were no differences between the right and left tibiae, the results of the two limbs were averaged. Torsional stiffness, maximum torque, and callus quantity were analyzed separately for the effect of time (2, 4, 8, and 12 weeks) on these parameters. These comparisons were performed with one-way analysis of variance (ANOVA) and were followed
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Orthop Res, Vol. 8, NO. 6, 1990
846
M . D . MARKEL ET A L .
by Tukey's studentized range post hoc t test when ANOVA revealed significant differences. In addition, the mean values for indentation stiffness, calcium content, new bone formation, and porosity for each type of tissue (periosteal, endosteal, cortex, and gap) were analyzed separately for the effect of time on these parameters with ANOVA and were followed by Tukey's studentized range post hoc t test when ANOVA revealed significant differences. The association between the mean values of indentation stiffness, calcium content, radiographically determined callus quantity, maximum torque, and torsional stiffness were quantitated with leastsquares regression. Data were correlated for each specific tissue (periosteal, endosteal, gap, or cortex) with 32 independent points (one for each dog) per correlation. Stepwise regression was also performed between the independent variables (calcium content, indentation stiffness, and callus quantity) and the dependent variables (maximum torque and torsional stiffness). The independent and dependent variables were chosen a priori to determine the association between local material properties and volume of callus and the structural properties of healing bone. All differences and associations were considered to be significant at a probability level of 95% (p < 0.05). All statistical analyses were performed with a
commercially available software program (SAS Institute, Inc., Cary, NC, U.S.A.).
RESULTS The local indentation stiffness of gap tissue increased linearly over time (Table 1). In periosteal tissue, stiffness increased up to 8 weeks and then plateaued at 12 weeks. Endosteal stiffness peaked at 8 weeks and then decreased by 12 weeks. Cortical stiffness decreased over time. The calcium content of gap tissue and periosteal callus increased over time (Table 1). The regression equations to describe dry weight of calcium change over time are linear for periosteal, endosteal, and gap tissue. There were no significant changes in cortical calcium content over time (Table 1). The percent unlabeled cortical bone decreased as a log function over time. New bone formation peaked in periosteal and endosteal callus at 4 weeks and then plateaued (periosteal) or declined (endosteal) by 12 weeks (Table 1). In gap tissue and cortical bone, new bone formation increased over time. Porosity decreased and plateaued in periostea1 callus, whereas endosteal callus porosity increased to greater than 2-week values by 12 weeks (Table 1). The porosity of gap tissue decreased with time but plateaued between 8 and 12 weeks.
TABLE 1. Local properties of healing osteotomy Weeks after surgery
Periosteal Mean
2 4 8 12
38.3" 48.6" 197.6' 138.2'
2 4 8 12
170.3" 155.8" 23 1.5' 255.3'
2 4 8 12
39.9" 63.4' 58.5' 59.6'
2 4 8 12
60.1" 36.4' 41.5' 40.4'
Gap SEM
Mean
Endosteal SEM
Mean
Cortex SEM
Indentation stiffness, region of interest stiffness (N/mm) 11.1 6.0 12.7" 31.3" 6.7 7.5 18.5" 6.0 48.3" 10.6 14.3 90.9' 21.4 98.9' 29.7 23.9 26.0 153.7' 40.2" 8.2 Calcium content (per dry weight), region of interest calcuim content (mg of calciumig of dry weight) 19.4 88.9" 31.9 178.8",b 13.2 10.3 86.5" 23.5 165.8" 16.2 6.0 229.5' 14.5 8.8 220. 2',' 13.4 232.0' 7.9 231.6' 23.5 Microradiographic new bone formation, region of interest new bone (%) 5.9 0.4" 0.4 25.0" 3.9 2.4 23.2' 7.3 42.4' 3.6 2.2 58.1' 3.1 35.2' 2.3 2.5 62.0" 1.6 13.0' 2.9 Porosity of bone regions, region of interest porosity (%) 5.9 99.6" 0.4 75.0" 3.9 2.4 76.8' 7.3 57.7' 3.6 2.2 41.9' 3.1 64.8' 2.3 2.5 38.0' 1.6 87.0' 2.9
Mean 892.7" 720.0". 589.5' 655.8'
SEM
'
261.3" 249.3" 255.0" 243.1"
8.5 11.1 2.5 7.3
3.2" 9.6" 20.2' 38.5"
0.8 1.5 1.8 2.0
11.5" 22.3' 21.3' 16.7'
1.o 1.2 3.8 2.1
Within a column for each parameter, superscripts of differing letters are significantly different from each other (p < 0.05). SEM = standard error of the mean.
J Orthop Res, Vol. 8, No. 6 , 1990
68.0 76.1 50.0 38.0
FRACTURE CALLUS RELATION TO TORSIONAL STRENGTH The 2-week osteotomies deformed in torsion but did not fracture, so the maximum torque could not be determined (Table 2). The maximum torque and torsional stiffness of the osteotomies increased over time and were significantly less strong than intact bone specimens at 12 weeks (Table 2). Radiographic callus formation peaked at 6 weeks and then gradually decreased (Table 3). At all time intervals, the lateral callus was greater than the medial, cranial, or caudal callus. In contrast, the medial callus was the smallest compared to the other three locations. The association between indentation stiffness and calcium content was moderately high (R2 = 0.66 and 0.50, p < 0.0001) for gap tissue and periosteal callus, respectively. The association between indentation stiffness of gap tissue and periosteal callus to the torsional strength of bone revealed moderate correlations with maximum torque (gap, R2 = 0.50, p < 0.0001 (Fig. 3, left); periosteal, R2 = 0.34, p < 0.05) and torsional stiffness (gap, R2 = 0.44, p < 0.0001; periosteal, R2 = 0.65, p < 0.0001). The association between the calcium content of the periosteal callus, endosteal callus, and gap tissue to torsional properties also revealed moderate correlations with the maximum torque (periosteal, R2 = 0.37, p < 0.05; endosteal, R2 = 0.31, p < 0.05; gap, R2 = 0.44, p < 0.005), and torsional stiffness (periosteal, R2 = 0.50, p < 0.0001; endosteal, R2 = 0.43, p < 0.0005; gap, R2 = 0.48, p < 0.0001 (Fig. 3, right)). Stepwise regression of the calcium content and indentation stiffness of gap tissue and periosteal callus to the maximum torque revealed that only indentation stiffness (gap, R2 = 0.50; p < 0.0001; periosteal, R2 = 0.34, p < 0.05) contributed signifTABLE 2. Torsional properties of healing osteotomy Torsional Values ~~~
Weeks after surgery Intact bone 2 4
8 12
Ultimate torque (Nm)
Torsional stiffness (Nm/rad)
Mean
SEM
Mean
SEM
28.5" NA 3.6* 15.6" 12.2'
2.3 NA 0.7 2.1 1.5
163.6" 0.9b 22.3'*'
15.3 0.2 9.8 10.5 7.6
77Sd 54.gd
SEM = standard error of the mean. NA = not applicable. Torsional properties weeks after surgery. Within a column, superscripts of differing letters are significantly different from each other (p < 0.05).
84 7
icantly to the regression when both parameters were in the model. In contrast, stepwise regression of the calcium content and indentation stiffness to the torsional stiffness of the bone revealed that calcium content alone contributed to the correlation coefficient in gap tissue (R2 = 0.44, p < O.OOOl), and local stiffness alone contributed significantly to the correlation coefficient in periosteal callus (R2 = 0.65, p < 0.0001). When calcium content, indentation stiffness, and radiographically determined callus quantity were included in stepwise regression, the callus quantity always contributed to the association between these parameters and torsional stiffness and the maximum torque of the bone. The callus quantity (gap, R2 = 0.21, p < 0.05; periosteal, R2 = 0.31, p < 0.05) with (gap, R2 = 0.33, p < 0.01) or without (periosteal, p > 0.05) indentation stiffness and without calcium content significantly contributed to the correlation coefficient with maximum torque (gap, R2 = 0.54, p < 0.005; periosteal, R2 = 0.31, p < 0.05). In contrast, calcium content (gap, R2 = 0.40, p < 0.001; periosteal callus, R2 = 0.12, p < 0.01) and callus quantity (gap, R2 = 0.21, p < 0.0001; periosteal, R2 = 0.53, p < 0.001) but not indentation stiffness significantly contributed to the model with torsional stiffness (gap, R2 = 0.61; p < 0.005; periosteal, R2 = 0.65, p < 0.0001). DISCUSSION Indentation testing as a means of determining compressive resistance (indentation stiffness) is a relatively simple and quick method. In contrast, most studies machine bone into various shapes to determine Young's modulus (10,13). The machining process is tedious and slow, thereby minimizing the number of sites that can be tested. Indentation testing requires only a surface to be tested and can readily be used in as many areas as is required for the study. Indentation testing has been used for determining the stiffness of the distal tibia (l), the proximal tibia (13), the patella (14), and periosteal callus in rats (5). Indentation with a consistent geometry resulted in similar-shaped load-deformation curves and is therefore an appropriate measure of local material stiffness. The changes in calcium content observed in the tibia1 osteotomies of this study are consistent with previous studies of rat fractures (2,5) and dog osteotomies (22). The gap tissue calcium content increased with time, by l 2 weeks it had not reached cortical values for calcium content. The
J Orthop Res, Vol. 8, No. 6 , 1990
M . D . MARKEL ET A L . TABLE 3. Radiographic callus formation Normalized radiographic callus, callus location Medial
Lateral
Anterior
Posterior
Weeks after surgery
Mean
SEM
Mean
SEM
Mean
SEM
Mean
SEM
2" 4 6 8 10 12
0.002",* 0.033",* 0.060", * 0.059". * 0.036"** 0.024",*
0.001 0.007 0.012 0.015 0.018 0.015
0.03",** 0.15',** 0.29c.** 0.26',** 0.22",** 0.15',**
0.007 0.024 0.041 0.021 0.032 0.035
0.02"'.** 0.09'*** 0.17",*** 0. 14c8*** 0.09',* 0.08',***
0.007 0.016 0.033 0.022 0.025 0.025
0.03"*** 0.1 Ia.b.** 0.20=3*** 0.18b,C,*** O.ll",b,* 0.08"****
0.012 0.022 0.034 0.028 0.035 0.036
SEM = standard error of the mean. Within a row, superscripts of differing number of asterisks are significantly different from each other (p < 0.05). Within a column, superscripts of differing letters are significantly different from each other (p < 0.05). Radiographic callus was normalized to the area of tibia at the region analyzed.
gap tissue calcium content would not be expected to reach cortical levels until the gap both had completely filled with new bone and also had completely remodeled (26). This remodeling may take from 1-3 years and was only just beginning by 12 weeks when the longest time group in this study was euthanized. The periosteal callus calcium content increased during the study but had plateaued by 12 weeks. This would be expected because periosteal callus is initially formed to anchor the bone ends and bridge the osteotomy. As the bone becomes stable, periosteal callus is resorbed by osteoclasts, therefore negating the need for progressive mineralization of the periosteal callus. Additionally, porosity of the periosteal callus initially decreased, which would be expected to be associated with increased calcium content, but then gradually increased as the callus was resorbed, probably minimizing any further increases in periosteal callus calcium content.
y=-5.69
+ 9.36 log x
p
