Journal of Orthopaedic Research 9422431 Raven Press, Ltd., New York 0 1991 Orthopaedic Research Society
Estimation of Mechanical Properties of Cortical Bone by Computed Tomography Susan M. Snyder and Erich Schneider M . E . Miiller Institute f o r Biomechanics, University of Bern, Bern, Switzerland
Summary: It is difficult to assess from conventional x-rays the amount of loading that a bone can tolerate. The question therefore was asked whether the mechanical properties of cortical bone could be estimated by using a computed tomography (CT) system typically employed in the clinical setting. In vitro cross sectional diaphyseal scans of adult human tibiae were made using a GE 9800 scanner and linear attenuation coefficients determined in several regions of the central cross sections. Samples from the mid-diaphyses of these tibiae were harvested, tested in three-point bending to failure, and mechanical properties as well as density and ash fraction determined. The respective relationships between CT measurements, mechanical properties, and physical properties were calculated using regression analysis. In addition, a solid calibration phantom (tricalciumphosphate) was scanned to evaluate the variability of CT measurements. The physical parameters measured in this study were found to be comparable with data from other authors but correlations were moderate to weak. Linear regression revealed the following correlation coefficients with CT data: r = 0.55 (Young’s modulus), r = 0.50 (strength), r = 0.65 (apparent density) and r = 0.46 (ash fraction). The correlation coefficients of these regressions for both linear and power fits were not significantly different. A high linear correlation (r = 0.99) was found between the chamber densities and the measured attenuation coefficients, but accuracy varied between 2 and 6%. The small range of specimen mechanical properties as well as the limitations inherent with the methods employed may explain these results. We conclude that clinical equipment as used in this study is not sufficient to accurately estimate the mechanical properties of cortical bone. Key Words: Cortical bone-Mechanical properties-Density-Computed tomography-Biomechanics.
alterations in blood supply (1 1) or bone stresses (4). Others are interested in such relationships in order to predict fracture risk of the hip, spine, or forearm in osteoporotic bone (8), to identify patients at risk for bone refracture after implant removal (6), or to determine strength reductions associated with metastatic defects (17). Finally, total joint replacement might benefit from utilization of geometrical as well as mechanical properties of the skeleton in the preoperative planning process. Bone density can be obtained in patients from CT
The ability to determine mechanical properties of cortical bone by a noninvasive technique such as computed tomography (CT) is attractive for a number of reasons. The effect of fixation devices on the mechanical properties of bone may be investigated, e.g., the problem of plate-induced osteopenia due to ~
Received September 27, 1989; accepted October 25, 1990. Address correspondence and reprint requests to Dr. E. Schneider at M. E. Muller Institute for Biomechanics, University of Bern, HP.0. Box 30, Solo, Bern, Switzerland.
422
ESTIMATION OF CORTICAL BONE PROPERTIES BY CT images, but accuracy is limited and errors range from 2 to 5% (13). Only special purpose CT scanners such as the one developed by Ruegsegger et al. (24) can achieve small errors and reproducibility on the order of 0.3% and are thus suited for prospective studies quantifying bone loss due to osteoporosis (25). Studies concerned with estimation of mechanical properties of trabecular bone using CT have already achieved reasonable success (1,29). Correlation coefficients of r = 0.94 and 0.69 between attenuation coefficients and Young’s moduli, respectively, were obtained for cubes having an edge length of 10 mm tested under compressive loading. Correlation with ultimate strength was found to be r = 0.74. These and other studies of trabecular bone (5) suggest that CT estimation may be a reasonable technique for noninvasive evaluation of bone mechanical properties. However when McBroom and co-workers (19) correlated CT values directly with vertebral compressive strength, the values were low ( r = 0.68). On the basis of their results, they were unable to demonstrate statistically significant predictions. It was the intent of the current study to determine if the mechanical properties of cortical bone could be estimated by means of a CT system typically employed in a clinical setting. A special solid calibration phantom (15) was used to quantitate the variability of the scanner. MATERIALS AND METHODS
The testing of human tibiae in this experiment involved CT scanning of the entire bone, followed by three point bending experiments (Fig. 1). Whole bone scans of three female (ages 55, 63, and 67 years) and four male human tibiae (ages 29, 55, 59, and 73 years) were performed. A total of 45 samples from the middiaphyses were harvested and tested in three point bending (modulus of elasticity, strength, and energy to failure). Physical properties of the samples (apparent density, dry defatted density, and ash fraction) were also determined. The results from the attenuation measurements, the mechanical tests, and determination of physical properties were then submitted to comparative analysis in order to determine the relationship between these variables. CT Scanning
In order to allow localization of the test “site”, a technique had to be used that provided references
423
visible on the specimens as well as in the CT images, without causing artifacts. Drill holes were found to be a simple and effective method. The test segment, centered around the middiaphysis, was marked by two coplanar drill holes at both ends. These holes were used as markers and allowed location of the central cross section in the long axis of the tibia as well as location of each sample within the central cross section. The holes were drilled in a radial direction by means of a 2 mm drill bit, 3 cm proximal and 3 cm distal to the middiaphysis. Because it is critical that both these holes be in the same cross sectional plane in order to fully appear on the CT image, a special aiming apparatus and technique were used. The bones were irrigated during drilling and kept moist during the entire procedure. After the preliminary marking procedure, scans were made with a GE 9800 CT scanner using the following system parameters: a pixel (picture element) size of 0.273 mm, a slice thickness of 1.5 mm, a pixel matrix of 512 X 512, and exposure factors of 120 kVp, 140 mA, and 3 s. Prior to each series of bone scans, a calibration phantom was used to assess the accuracy of this particular CT scanner. A solid phantom (15) was selected, because the range of K,HPO, calibration solutions of the liquid phantom used by Genant et al. (10) is limited and would necessitate extrapolation for cortical bone. This was not the case for the solid phantom, which consisted of seven full cylinders, 2.5 cm in diameter, manufactured from varying weight percentages (1070) of tricalcium phosphate (attenuation properties similar to hydroxyapatite) and polymethyl metacrylate. The phantom densities (cylinder weight divided by volume) were determined to vary from 1.24 to 2.05 g/cm3. Computed tomography allows display and evaluation of the attenuation of x-ray beams at discrete locations within each transverse slice. The polyenergetic nature of the x-ray source, however, causes the attenuation of the x-ray beam to deviate from exponential form. The preferential attenuation of lower energy photons that results when the beam passes through an object produces undesirable distortions of the projections. A water bath is often used to better simulate the in vivo cross section when scanning bone specimens and to avoid high frequency signals at the airhone interface (“ringing” artifacts). The calibration phantom was, therefore, scanned with and without a water bath. Identical measurements were taken on two different
J Orthop Res. Vol. 9, No. 3, 1991
S . M . SNYDER AND E. SCHNEIDER
424
CT Scanner
Samples cut longitud with ISOMET saw
Scans taken at middiaphysis
a
sectioned with band saw
mfl coefficients of Determination attenuation at
sample locations on CT image
Samples trimmed with microtome
& a Three-~in t bending test
Mass and volume measured to determine sample densities
FIG.1. Overview of methods used for specimen preparation and analysis.
days to detect scanner variations. Scans were taken at two different locations within each cylinder. The linear attenuation coefficient was determined at four randomly selected locations within each cross section of the cylinder for each of the measuring conditions. The CT data of the seven phantom cylinders were then linearly correlated with density using least squares regression analysis to obtain a calibration curve for the scanner. The error encountered when utilizing the CT scanner for density measurements was calculated as two standard deviations divided by the mean value for each concentration. After verification that no significant variability of measurements in the long axis of the bone was present, attenuation measurements from three adjacent scan slices centered around the middiaphysis were used for the subsequent analysis. The rectangular region of interest (ROI) corresponded to the dimensions of the actual bone specimen (-2 x 2 mm). Knowing that the actual resolution of the scanner (0.5-1 mm) is considerably less than the pixel resolution of 0.273 mm, a sufficient number of pixels (-50) was contained in each ROI. Three scans were taken at both ends of the test segment to ensure localization of both reference drill holes in one image, but only one of them was used for subsequent determination of sample coordinates. The results of the CT measurements were ex-
J Orthop Res, Voi. 9, N o . 3, 1991
pressed in terms of the attenuation coefficient p,, a dimensionless number relating the linear attenuation coefficient of the material to the same coefficient of water. It is expressed in Hounsfield units (HU). Attenuation was evaluated by averaging the entire ROI (Fig. 2). In addition, each ROI was averaged over the three central slices. Mechanical Testing
After completion of the scanning, bone samples were harvested for three point bending tests. Cuts perpendicular to the longitudinal axis through the drill holes at the proximal and distal locations were made with a band saw to produce a bone segment 6 cm in length (Fig. 1). Using an ISOMET (Model 11-1180) low speed saw, cuts were made perpendicular to the bone surface and parallel to the longitudinal axis of the bone segment. Samples in slight excess of 2 mm in width were obtained at various locations around the circumference of the bone. Sample locations were numbered according to approximate anatomical position with number 1 signifying the most anterior position and increasing sample numbers representing the medial, posterior, and lateral positions, respectively (Fig. 2). In some tibiae, only six samples could be harvested. The distances between the periosteal edges of the samples and the drill holes and the distance between the two drill holes were determined by means of a caliper.
425
ESTIMATION OF CORTICAL BONE PROPERTIES BY CT ROI 1
Sample 1
FIG 2. Location of samples around bone circumference (left) and sample window location in CT image for evaluation of attenuation coefficient (right).
1 hole
Drill hol
3
4
These distances were used to determine, by means of the law of cosines, the sample locations based on coordinate systems defined by the drill holes. The variation between repeated coordinate measurements using this technique was found to be
Estimation of Mechanical Properties of Cortical Bone by Computed Tomography Susan M. Snyder and Erich Schneider M . E . Miiller Institute f o r Biomechanics, University of Bern, Bern, Switzerland
Summary: It is difficult to assess from conventional x-rays the amount of loading that a bone can tolerate. The question therefore was asked whether the mechanical properties of cortical bone could be estimated by using a computed tomography (CT) system typically employed in the clinical setting. In vitro cross sectional diaphyseal scans of adult human tibiae were made using a GE 9800 scanner and linear attenuation coefficients determined in several regions of the central cross sections. Samples from the mid-diaphyses of these tibiae were harvested, tested in three-point bending to failure, and mechanical properties as well as density and ash fraction determined. The respective relationships between CT measurements, mechanical properties, and physical properties were calculated using regression analysis. In addition, a solid calibration phantom (tricalciumphosphate) was scanned to evaluate the variability of CT measurements. The physical parameters measured in this study were found to be comparable with data from other authors but correlations were moderate to weak. Linear regression revealed the following correlation coefficients with CT data: r = 0.55 (Young’s modulus), r = 0.50 (strength), r = 0.65 (apparent density) and r = 0.46 (ash fraction). The correlation coefficients of these regressions for both linear and power fits were not significantly different. A high linear correlation (r = 0.99) was found between the chamber densities and the measured attenuation coefficients, but accuracy varied between 2 and 6%. The small range of specimen mechanical properties as well as the limitations inherent with the methods employed may explain these results. We conclude that clinical equipment as used in this study is not sufficient to accurately estimate the mechanical properties of cortical bone. Key Words: Cortical bone-Mechanical properties-Density-Computed tomography-Biomechanics.
alterations in blood supply (1 1) or bone stresses (4). Others are interested in such relationships in order to predict fracture risk of the hip, spine, or forearm in osteoporotic bone (8), to identify patients at risk for bone refracture after implant removal (6), or to determine strength reductions associated with metastatic defects (17). Finally, total joint replacement might benefit from utilization of geometrical as well as mechanical properties of the skeleton in the preoperative planning process. Bone density can be obtained in patients from CT
The ability to determine mechanical properties of cortical bone by a noninvasive technique such as computed tomography (CT) is attractive for a number of reasons. The effect of fixation devices on the mechanical properties of bone may be investigated, e.g., the problem of plate-induced osteopenia due to ~
Received September 27, 1989; accepted October 25, 1990. Address correspondence and reprint requests to Dr. E. Schneider at M. E. Muller Institute for Biomechanics, University of Bern, HP.0. Box 30, Solo, Bern, Switzerland.
422
ESTIMATION OF CORTICAL BONE PROPERTIES BY CT images, but accuracy is limited and errors range from 2 to 5% (13). Only special purpose CT scanners such as the one developed by Ruegsegger et al. (24) can achieve small errors and reproducibility on the order of 0.3% and are thus suited for prospective studies quantifying bone loss due to osteoporosis (25). Studies concerned with estimation of mechanical properties of trabecular bone using CT have already achieved reasonable success (1,29). Correlation coefficients of r = 0.94 and 0.69 between attenuation coefficients and Young’s moduli, respectively, were obtained for cubes having an edge length of 10 mm tested under compressive loading. Correlation with ultimate strength was found to be r = 0.74. These and other studies of trabecular bone (5) suggest that CT estimation may be a reasonable technique for noninvasive evaluation of bone mechanical properties. However when McBroom and co-workers (19) correlated CT values directly with vertebral compressive strength, the values were low ( r = 0.68). On the basis of their results, they were unable to demonstrate statistically significant predictions. It was the intent of the current study to determine if the mechanical properties of cortical bone could be estimated by means of a CT system typically employed in a clinical setting. A special solid calibration phantom (15) was used to quantitate the variability of the scanner. MATERIALS AND METHODS
The testing of human tibiae in this experiment involved CT scanning of the entire bone, followed by three point bending experiments (Fig. 1). Whole bone scans of three female (ages 55, 63, and 67 years) and four male human tibiae (ages 29, 55, 59, and 73 years) were performed. A total of 45 samples from the middiaphyses were harvested and tested in three point bending (modulus of elasticity, strength, and energy to failure). Physical properties of the samples (apparent density, dry defatted density, and ash fraction) were also determined. The results from the attenuation measurements, the mechanical tests, and determination of physical properties were then submitted to comparative analysis in order to determine the relationship between these variables. CT Scanning
In order to allow localization of the test “site”, a technique had to be used that provided references
423
visible on the specimens as well as in the CT images, without causing artifacts. Drill holes were found to be a simple and effective method. The test segment, centered around the middiaphysis, was marked by two coplanar drill holes at both ends. These holes were used as markers and allowed location of the central cross section in the long axis of the tibia as well as location of each sample within the central cross section. The holes were drilled in a radial direction by means of a 2 mm drill bit, 3 cm proximal and 3 cm distal to the middiaphysis. Because it is critical that both these holes be in the same cross sectional plane in order to fully appear on the CT image, a special aiming apparatus and technique were used. The bones were irrigated during drilling and kept moist during the entire procedure. After the preliminary marking procedure, scans were made with a GE 9800 CT scanner using the following system parameters: a pixel (picture element) size of 0.273 mm, a slice thickness of 1.5 mm, a pixel matrix of 512 X 512, and exposure factors of 120 kVp, 140 mA, and 3 s. Prior to each series of bone scans, a calibration phantom was used to assess the accuracy of this particular CT scanner. A solid phantom (15) was selected, because the range of K,HPO, calibration solutions of the liquid phantom used by Genant et al. (10) is limited and would necessitate extrapolation for cortical bone. This was not the case for the solid phantom, which consisted of seven full cylinders, 2.5 cm in diameter, manufactured from varying weight percentages (1070) of tricalcium phosphate (attenuation properties similar to hydroxyapatite) and polymethyl metacrylate. The phantom densities (cylinder weight divided by volume) were determined to vary from 1.24 to 2.05 g/cm3. Computed tomography allows display and evaluation of the attenuation of x-ray beams at discrete locations within each transverse slice. The polyenergetic nature of the x-ray source, however, causes the attenuation of the x-ray beam to deviate from exponential form. The preferential attenuation of lower energy photons that results when the beam passes through an object produces undesirable distortions of the projections. A water bath is often used to better simulate the in vivo cross section when scanning bone specimens and to avoid high frequency signals at the airhone interface (“ringing” artifacts). The calibration phantom was, therefore, scanned with and without a water bath. Identical measurements were taken on two different
J Orthop Res. Vol. 9, No. 3, 1991
S . M . SNYDER AND E. SCHNEIDER
424
CT Scanner
Samples cut longitud with ISOMET saw
Scans taken at middiaphysis
a
sectioned with band saw
mfl coefficients of Determination attenuation at
sample locations on CT image
Samples trimmed with microtome
& a Three-~in t bending test
Mass and volume measured to determine sample densities
FIG.1. Overview of methods used for specimen preparation and analysis.
days to detect scanner variations. Scans were taken at two different locations within each cylinder. The linear attenuation coefficient was determined at four randomly selected locations within each cross section of the cylinder for each of the measuring conditions. The CT data of the seven phantom cylinders were then linearly correlated with density using least squares regression analysis to obtain a calibration curve for the scanner. The error encountered when utilizing the CT scanner for density measurements was calculated as two standard deviations divided by the mean value for each concentration. After verification that no significant variability of measurements in the long axis of the bone was present, attenuation measurements from three adjacent scan slices centered around the middiaphysis were used for the subsequent analysis. The rectangular region of interest (ROI) corresponded to the dimensions of the actual bone specimen (-2 x 2 mm). Knowing that the actual resolution of the scanner (0.5-1 mm) is considerably less than the pixel resolution of 0.273 mm, a sufficient number of pixels (-50) was contained in each ROI. Three scans were taken at both ends of the test segment to ensure localization of both reference drill holes in one image, but only one of them was used for subsequent determination of sample coordinates. The results of the CT measurements were ex-
J Orthop Res, Voi. 9, N o . 3, 1991
pressed in terms of the attenuation coefficient p,, a dimensionless number relating the linear attenuation coefficient of the material to the same coefficient of water. It is expressed in Hounsfield units (HU). Attenuation was evaluated by averaging the entire ROI (Fig. 2). In addition, each ROI was averaged over the three central slices. Mechanical Testing
After completion of the scanning, bone samples were harvested for three point bending tests. Cuts perpendicular to the longitudinal axis through the drill holes at the proximal and distal locations were made with a band saw to produce a bone segment 6 cm in length (Fig. 1). Using an ISOMET (Model 11-1180) low speed saw, cuts were made perpendicular to the bone surface and parallel to the longitudinal axis of the bone segment. Samples in slight excess of 2 mm in width were obtained at various locations around the circumference of the bone. Sample locations were numbered according to approximate anatomical position with number 1 signifying the most anterior position and increasing sample numbers representing the medial, posterior, and lateral positions, respectively (Fig. 2). In some tibiae, only six samples could be harvested. The distances between the periosteal edges of the samples and the drill holes and the distance between the two drill holes were determined by means of a caliper.
425
ESTIMATION OF CORTICAL BONE PROPERTIES BY CT ROI 1
Sample 1
FIG 2. Location of samples around bone circumference (left) and sample window location in CT image for evaluation of attenuation coefficient (right).
1 hole
Drill hol
3
4
These distances were used to determine, by means of the law of cosines, the sample locations based on coordinate systems defined by the drill holes. The variation between repeated coordinate measurements using this technique was found to be
