JOURNAL OF BONE AND MINERAL RESEARCH Volume 7, Number 10, 1992 Mary Ann Liebert, h e . , Publishers
Mechanical Properties of Trabecular Bone Within and Adjacent to Osseous Metastases JOHN A. HIPP,' ANDREW E. ROSENBERG,' and WILSON C. HAYES'
ABSTRACT Despite radiographic and histologic evidence of trabecular bone density changes within and adjacent to osseous metastases, there currently exist no data to demonstrate whether these changes are important in predicting the risk of fracture. To determine if these density changes result in significant reductions in mechanical properties, trabecular bone specimens were prepared from lower thoracic and lumbar vertebrae from two cadavers with radiographic, gross, and histologic evidence of lytic and/or blastic osseous metastases. Each specimen was classified as normal, lytic, or blastic based on appearance in fine-grain radiographs of 8-9 mm thick coronal plane sections. Specimens were tested to failure in uniaxial compression, and tissue and apparent densities were measured. Mean tissue densities were within normal ranges. The mean apparent density for all specimens combined was within the normal range for human vertebrae, and the mean apparent density for radiographically normal (0.131 g/ml) and lytic (0.111 g/ml) specimens was less than the mean apparent density of blastic (0.182 g/ml) specimens (p < 0.02). The moduli of lytic and blastic specimens were less than for normal specimens (p < 0.025). The strength of lytic specimens was less than normal (p = 0.0571, but the strength of blastic specimens was not (p > 0.1). Apparent density explained significant fractions of the variations in both modulus (p < 0.001) and strength (p < 0.001). The data suggest that blastic changes associated with osseous metastases to trabecular bone disrupt the normal dependence of trabecular mechanical properties on apparent density, but lytic changes do not. These data also suggest that fracture risk predictors that utilize bone density to estimate stiffness or strength should adjust for the effects of metastases.
INTRODUCTION s THE SURVIVAL TIME for patients with cancer increases, the need to manage osseous metastases has become a
A
more frequent and important clinical problem. The advantages of prophylactic stabilization of osseous defects compared with the management of pathologic fractures include increased life expectancy, reduced pain, and faster return to mobility.(l.'j Predicting which osseous defects should be prophylactically stabilized remains problematic and has been addressed in several ~ l i n i c a l ' ~ -and ' ~ in vitro studies. ('-'01 However, reliable and comprehensive criteria for prophylactic stabilization have yet to be developed. As with most structures, the strength of a bone is a function of geometric variables, material properties, and func-
tional demands. Several studies have considered the significance of defects with regular geometries in models of cortical bone in which the bone was assumed to have homogeneous material properties.(n-lO1Two of these studies have further suggested the importance of density changes adjacent to cortical However, no studies have considered the mechanical properties of trabecular bone from within and around osseous metastatic defects. This is an important concern, since the spine is the most common site for osseous metastases from many primary tumors(1'-'41 and metastases to the spine almost always involve trabecular bone. ( 1 5 ) Although a substantial literature is available on the mechanical properties of normal and osteoporotic trabecular bone, (l6-IP1 no studies have specifically reported the me-
'Orthopaedic Biomechanics Laboratory, Department of Orthopaedic Surgery, Charles A. Dana Research Institute. Beth Israel Hospital and Harvard Medical School, Boston, Massachusetts. 'James Homer Wright Pathology Laboratories, Department of Pathology, Massachusetts General Hospital, Boston.
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chanical properties of bone compromised by metastatic disease. For normal trabecular bone, power-law relations between trabecular bone density and strength or stiffness~17~1n~10’ have been described. However, there is considerable scatter in the coefficients for these relationships. (’I1 For bone compromised by metastases, the relationship between bone density and strength may depend on the primary tumor from which the metastasis arose. A variety of mechanisms for the bone resorption and formation that occur with metastases from various primary tumors have been suggested. ( l l m ) The radiologic and histologic evidence of lytic and/or blastic changes to bone within and adjacent to osseous metastases[141leads to the hypothesis that the mechanical properties could be significantly altered and thus could be an important factor in predicting fracture risk. To address this question, our first objective was to determine if lytic and blastic changes to trabecular bone alter its mechanical properties. We also wished to determine if relationships between trabecular bone density and strength or stiffness are altered by metastatic involvement.
MATERIALS AND METHODS Lumbar and thoracic vertebrae were obtained from two donors with osseous metastases noted on the medical histories. One donor was a 78-year-old female, with the cause of death listed as lung cancer, breast cancer, and melanoma. The other donor was a 82-year-old female with the cause of death listed as breast cancer. Anteroposterior (AP) and mediolateral (ML) radiographs of the intact thoracolumbar spine were obtained and used to identify metastases. Biopsies were obtained from sites of metastases by passing a 2 mm coring tool through the pedicle into the tumor sites. Decalcified, hematoxylin- and eosin-stained sections were prepared from each biopsy and analyzed by an orthopedic pathologist. Quantitative computed tomographic (QCT) scans were obtained for vertebrae with radiographically evident metastases and for the adjacent vertebrae. Vertebrae were immersed in a saline bath during scanning. Scans were obtained with a GE9800 scanner using 3.0 mm thick slices, 5.0 mm table increments, and a pixel size of 0.59 mm. A dipotassium phosphate phantom was included in the scans to allow quantitative analysis of bone density. CT data were transferred to SUN workstations (SUN Microsysterns, Mountain View, CA) for analysis of bone density. Individual vertebrae were isolated and embedded in a fast-curing foam (LiteCast; Isocast Systems, Inc., Clackamas, OR) to facilitate sectioning into specimens for mechanical testing. Care was taken to maintain appropriate anatomic orientation. Two coronal slabs were obtained through the centrum of each vertebrae using a band saw. Each slab was 6-9 mm thick. The end plates were not included. The slabs were analyzed visually for the presence of discoloration and texture characteristic of the presence of tumor.‘”’ Each slab was then radiographed (Faxitron; Hewlett-Packard, McMinnville, OR) using fine-grain film (Kodak X-Omat TL; Eastman Kodal Co., Rochester, NY)
to localize density changes characteristic of metastatic involvement. Cubic specimens approximately 8 mm wide in each dimension were then cut from each slab using a lowspeed diamond wafering saw (Isomet; Beuhler, Ltd., Lakebluff, IL), again being careful to maintain anatomic orientation. Cubes were cut such that mineralized tissue was present throughout the cube. Cubes in which large regions were completely demineralized were not utilized for testing. As a result of this protocol, specimens were subject to two freeze-thaw cycles before mechanical testing. Specimens were thawed to prepare the cubes, frozen, and then thawed just before testing. Specimens were not embalmed and were tested fully hydrated at room temperature. The location of each cube was carefully marked on the radiograph of the parent slab, and the overall radiographic appearance of the cube relative to all other sites for that donor was recorded as normal, lytic, or blastic. Using the marked radiographs, the approximate location of each cube was determined in the transverse C T data. Using SUNVISION image-processing software (SUN Microsysterns, Mountain View, CA) and the dipotassium phosphate phantom, the average density (expressed as g/ml of dipotassium phosphate) was determined for each cube. A total of 134 cubes of trabecular bone were prepared, evaluated densitometrically, and tested mechanically. The dimensions of each cube were measured to the hundredth of a millimeter three times using digital calipers and the average values calculated. Cubes were mechanically tested in uniaxial compression between rigid platens using a servohydraulic materials testing system (model 1331; Instron Corp., Canton, MA, with Series 3200 controller; Interlaken Technology Corp., Eden Prairie, MN). Displacement was measured using an extensometer connected to the platens, thereby eliminating the need to adjust for system compliance. Strain was calculated by dividing the platen displacement by the initial height. Cubes were tested to 5% strain at a strain rate of 0.2 s-l. Specimens were tested along the craniocaudal axis. Stress and strain data were recorded for each test using a personal computerbased data acquisition system (Dell 386SX; Dell Computers, Austin, TX, with a Data Translation DT2801A; Data Translation, Marlboro, MA, and Labtech Notebook software; Laboratory Technologies, Wilmington, MA). From these data, the ultimate stress (o,lt) was recorded, and a linear regression was fit to the data from 0 . 3 to~ ~ ~ ~ 0.70,1t. This linear regression was used to calculate the 0.2% yield stress. Densities for each specimen were determined following mechanical testing. Nonmineralized tissue was removed from specimens by ultrasonic treatment in a 0.5% solution of sodium hypochlorite and rinsing with a water jet. These two steps were repeated several times until there was no visible evidence of nonmineralized tissues. Wet weight was determined after thorough degassing. Apparent density was determined as the wet weight divided by the sample volume (volume determined before testing). Bone tissue volume was calculated as the hydrated weight less the submerged weight. Tissue density was calculated as the hydrated tissue mass divided by the bone tissue volume. Tissue densities less than 1.6 were considered to represent in-
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PROPERTIES OF TRABECULAR BONE WITH METASTASES
FIG. 1. High-resolution radiograph of an 8 mm thick slice through the fourth lumbar vertebrae of a cadaveric specimen for which the cause of death was listed as breast cancer. The section is in the coronal plane.
complete removal of marrow contents and thus unreliable density measurements. These specimens were excluded from the remainder of the analysis. Statistical analysis of the data was completed using RS1 and RS/Explore software (BBN Software Products Corp., Cambridge, MA). One-way analysis of variance was used to determine if the radiographic appearance was a predictor of apparent density. The hypothesis that lytic and blastic changes alter mechanical properties was investigated by one-way analyses of variance of the effect of radiographic appearance on modulus or strength. The hypothesis that the relationships between density and mechanical properties were different for bone compromised by tumor was investigated by analysis of covariance of the effects of radiographic appearance and apparent density on mechanical properties. Linear regressions were used to determine how well QCT was able to predict density. In several instances, the one-way analysis of variance was completed using medians rather than means. When data are outlier prone and/ or the variances between groups are not equal, analysis using medians is the preferred method. i z s ) Moreover, the use of medians is a conservative approach since it is less sensitive and produces lower significance levels than when using means.c2s1In most cases, the bisquare method was used to determine regression equation coefficients, since it tends to estimate coefficients with less sensitivity to outliers in the data. This is also a conservative approach and is less likely to report statistical significance that does not actually exist.'z61
RESULTS Pathologic analysis of the biopsies demonstrated metastatic deposits consistent with spread from breast cancer in both donors. There was no evidence of pathologic fractuires or other deformities. A few areas of increased den-
TABLE1. DISTRIBUTION OF TRABECLJLAR BONECUBES WITHIN THE THREERADIOGRAPHIC APPEARANCE CATEGORIES
Donor
Normal
Lytic
Blastic
Total
HI01 1
45 19 64
14 37 51
12 7
71 63 134
H937 Both
19
sity were radiographically evident in AP and ML plane films of the intact spines in each individual. From visual observation of radiographs of the thick slabs cut from each vertebrae, the trabecular bone appeared generally mottled, with several areas of locally increased density (Fig. 1) and a few areas of obvious lysis. A periosteal bone response was noted in most slabs, and involvement of the pedicles was evident in two vertebrae. The qualitative classification of cubes into normal, lytic, or blastic was not always clear. Several cubes appeared to be of mixed pathology and partly normal. In these cases the cubes were classified toward the extreme (i.e., a partly blastic cube was classified as blastic). More cubes were classified as radiographically normal than specimens classified as lytic or blastic (Table 1). Because 26 cubes had measured tissue densities less than 1.6,these data were eliminated from further consideration since low tissue density was assumed to be due to incomplete removal of marrow and thus unreliable. There was no obvious relationship between excluded specimens and donor or radiographic appearance. After exluding unreliable density data, the tissue densities ranged from 1.61 to 2.69 g/ml (mean 1.95; standard deviation, SD, 0.20). There were six specimens with tissue densities greater than 2 g/ml, two of which were classified as radiographically normal; the remaining four were classified as lytic. Apparent density data for both donors spanned a wide range
HIPP ET AL.
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(0.038-0.465 g/ml), and the distribution of densities was heavily weighted toward the low-density range (mean = 0.130 g/ml, SD 0.062). The mean apparent densities for the two donors were significantly different, both for all cubes (0.154 versus 0.108 g/ml, p = 0.0065) and for only radiographically normal specimens (0.150 versus 0.0924 g/ml, p = 0.0012).Tissue density explained only 4.5% of the variation in apparent density (p = 0.027), based upon linear regression with a bisquare estimation procedure. Based on one-way analysis of variance, radiographic appearance explained only 4.4% of the variation in tissue densities (p = 0.095), and there were no significant differences between means of the radiographic appearance groups. Radiographic appearance explained slightly more (13.4%) of the variation in apparent density (p = 0.0005). The value of apparent densities for normal and lytic specimens (Fig. 2) were significantly less than for blastic specimens (p = 0.013 and 0.0007 for lytic and blastic specimens, respectively). All points that fell outside the 95% confidence intervals for each group had apparent densities greater than expected. Before mechanical testing, each of the three dimensions of the cubic specimens were measured three times. The mean standard deviation of these measurements was 0.06 mm. Almost all stress-strain curves had both a linear region before failure and a definite ultimate stress (Fig. 3). There was greater uncertainty in the definition of a peak load with some of the specimens that failed at very low loads. Overall, a significant linear relation between the yield stress and the ultimate stress was found (oyld = 0 . 9 3 9 ~ ~-10.022; ~ r' = 0.99). A moderate linear correlation was found between ultimate stress and modulus (oulr = 0.0126E + 0.388; r' = 0.68) and yield stress versus modulus (uyld = 0.0119E + 0.33; r' = 0.70). Analysis of covariance was used to test the hypothesis that the presence of tumor affected bone modulus. This test was done twice, first using linear regressions, and then using linear regression on the logarithms of the data. The first test indicated that both radiographic appearance and apparent density affected elastic modulus (p c 0.001 for radiographic appearance and 0.0048 for apparent density). The slope of linear regressions relating apparent density to modulus appeared to be strongly influenced by high-density specimens and was not statistically different between the radiographic appearance groups (Fig. 4). In addition. the correlation coefficients for these regressions were very low (rl = 0.086, 0.14, and 0.11 for normal, lytic, and blastic specimens, respectively). However, the average modulus for radiographically normal specimens was significantly higher than for lytic or blastic cubes (p = 0.0018 and O.ooO1, respectively; Fig. 5 ) . Average moduli for lytic specimens were not statistically different than for blastic specimens. To address the issue of whether a power law would explain relationships between density and modulus better than a linear one, we also completed an analysis of covariance using the logarithms of apparent density and modulus. Compared to the residuals from the linear regressions using untransformed data, the residuals from the regressions to log data were greater and not as randomly distributed. The regressions using log data explained even
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Radiographic Appearance Group FIG. 2. Simultaneous comparison of apparent density between radiographic appearance groups. The small boxes show the mean apparent density for each radiographic appearance group, and the bars attached to each box show the standard deviations. These error bars overlap if the difference between two means is not significant at the 5 % level. Significant differences are determined using Bonferroni's simultaneous confidence intervals for all comparisons. The grand average for all specimens is shown by the horizontal line, and the error bounds for this average are shown by the dashed lines.
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STRAIN FIG. 3. Compressive stress-strain curve for a radiographically normal specimen. The yield stress, ultimate stress, and linear regression line used to calculate modulus are labeled.
1169
PROPERTIES OF TRABECULAR BONE WITH METASTASES
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APPARENT DENSITY (g/ml) FIG. 4. Uniaxial compressive modulus as a function of apparent density, grouped by radiographic appearance. Radiographically normal specimens are represented by solid squares, lytic specimens by open circles, and blastic specimens by open triangles. The linear regressions to the data for each radiographic appearance group are also shown. A thin solid line is used for the normal specimens, a heavy double line for lytic specimens, and a dashed line for blastic specimens. The slopes of these regression lines are not statistically different at the 5% level.
less of the variation. Regressions using log data also demonstrated no significant difference in slope between the radiographic appearance groups. After adjusting for apparent density using analysis of covariance, there was little evidence that radiographic appearance affected maximum stress (p = 0.061). However. apparent density affected the maximum stress after adjusting for radiographic appearance (p < 0.001). As with modulus data, there were several extreme observations with abnormally high densities. Linear or power-law regressions of density versus strength data were no better than found for density versus modulus. There was no difference between the mean yield stress or maximum stress for normal versus lytic or blastic specimens. Analysis of covariance of the effect of radiographic appearance and apparent density on QCT density suggests little dependence of QCT density on radiographic appearance (p = 0.054), but a strong dependence of QCT density on apparent density (p < 0.001). As with other parameters, specimens with high densities appeared as outliers. Robust (bisquare) linear regression of QCT density as a function of apparent density suggest moderate linear relationships, and the slope of the line fit to the data for blastic specimens (494 mg/ml per g/ml) was significantly greater (p = 0.0002)than the slope for normal specimens (218 mg/ml per g/ml).
DISCUSSION
1151
100'
RADIOGRAPHIC APPEARANCE
FIG. 5. Mean modulus for normal, lytic, and blastic specimens. Standard deviations are shown by the error bars. Using simultaneous comparisons, the modulus of radiographically normal specimens was different from that for lytic (p = 0.0013) or blastic (p = 0.023) specimens.
Although limited in scope, these measurements demonstrate that significant reductions in mechanical properties can accompany invasion of trabecular bone by tumor cells. Our data do not demonstrate whether the relationship between density and mechanical properties is changed by the presence of tumor. As far as we are aware, these are the first experiments to report measurements of the mechanical properties of trabecular bone from within and adjacent to osseous metastases. This study had several limitations. Since trabecular bone specimens from only two individuals were tested, it is not clear whether other primary tumors, or other pathologic manifestations of breast or lung metastases, have comparable effects on trabecular bone. The extent of tumor involvement in our bone specimens was difficult to determine from radiographs. Overall, the radiographic appearance of most of the slabs cut from each vertebrae was consistent with the mixed lytic and blastic characteristics that have been reported for breast cancer."'] Good agreement between fine-grain radiographic analysis of 4 mm thick coronal sections through vertebral bodies and histologic analysis has been reported in other studies. (I2) Although radiographic appearance should agree with histologic analysis, it does not provide a quantitative measurement of the extent of tumor involvement in each tested trabecular bone specimen. This was the most significant shortcoming of this study. Other methods that would quantify the extent of tumor were considered. It was not practical to analyze bone adjacent to each cube histologically, because the processing required to cut cubic specimens from vertebral
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bodies destroyed any useful cellular detail. Thus, we had nation. In addition, a greater variation in fat content may to use qualitative and subjective estimates of tumor in- occur with metastatically compromised bone. With singlevolvement in each specimen. This was complicated by the energy QCT, a variable fat content would adversely affect presence of both lytic and blastic changes in each donor measurement of bone density.(a01Thus dual-energy QCI’ and the greater incidence of blastic specimens from one may be advantageous in future studies of this type. To better identify fracture risk predictors that account donor compared to the other. In cases of complete bone lysis, it was of course not possible to test tissue within that for trabecular bone density changes within and adjacent to region, but it was possible to say which specimens directly osseous metastases, changes in the relationship between bordered that region and investigate the hypothesis that density and mechanical properties should be quantified. bone juxtaposed to regions of tumor lysis would be me- Based upon this study, a conservative adjustment for the effects of blastic changes in trabecular bone might be to chanically compromised by tumor. Published equations relating mechanical properties to place a limit on the upper bound of trabecular density, density are not always consistent since both linear and perhaps using the average density from radiographically power-law regressions are reported and the coefficients of normal trabecular bone sites. In practice, this could be acthese regressions vary considerably. (’I1 These relationships complished using interactive array editors to lower the denmay depend on species, anatomic location, orientation, sity of radiographically blastic regions to the average denand the method by which apparent density is mea- sity of radiographically normal regions. This prevents the ~ u r e d . ( ~ ’It. ~is~thus ’ difficult to show whether the radio- increased density of blastic regions from inappropriately graphically normal specimens tested in this study had nor- raising structural predictors that are weighted by density. mal mechanical properties. The mean tissue density was ACKNOWLEDGMENTS within reported normal ranges, but the standard deviation in this measure was greater than has been reported for norThis study was supported by NIH Grant No. CAN21 1mal bone.”’1 It is not clear whether this is because tumor physically altered the bone tissue or whether specimens 05, Biomechanics of Metastatic Defects in Bone, and the were not thoroughly cleaned of marrow components. The Maurice E. Meuller Professorship in Biomechanics at Harmeasured apparent densities for cubes classified as radio- vard Medical School (Dr. Hayes). The contributions of graphically normal were slightly higher than has been re- Dheera Ananthakrishnan, Alexa Page, and Steve Piazza to ported for radiographically normal vertebrae from an the preparation and testing of bone specimens are grateelderly human population. I1s.’pl The distribution of appar- fully acknowledged. ent densities in each of the radiographic appearance groups (Fig. 2), demonstrates that all the points that fell outside REFERENCES the 95% confidence intervals had apparent densities greater than expected. This suggests that it is difficult to I . Habermann ET, Sachs R. Stern RE, Hirsh DM, Anderson assess osteoblastic changes in trabecular bone even from WJ 1982 The pathology and treatment of metastatic disease fine-detail in vitro radiographs. of the femur. Clin Orthop 169:70-82. Elastic modulus predicted the ultimate compressive 2. Sherry HS, Levy RN, Siffert RS 1982 Metastatic disease of strength of trabecular bone compromised by tumor as well bone in orthopedic surgery. Clin Orthop 169:44-52. (r’ = 0.68) as has been reported for other sites.(”’ The 3. Beals RK. Lawton GD. Snell WE 1971 Prophylactic internal slope of linear regressions between density and the meafixation of the femur in metastatic breast cancer. Cancer 28: 1350- 1354. sured mechanical parameters appeared to be strongly influ4. Fidler M 1981 Incidence of fracture of metastases in long enced by the presence of outliers with high densities. The bones. Acta Orthop Scand 52623-627. slopes of these regression lines for the different radio5 . Bunting R , Larnont-Havers W, Schweon D. K h a n A 1985 graphic appearance groups were not statistically different. Pathologic fracture risk in rehabilitation of patients with For our data. linear regressions of density versus modulus bony metastases. Clin Orthop 192222-227. explained more of the variation in the data than did 6 . Keene JS, Sellinger DS, McBeath AA, Engber WD 1986 power-law fits. Our data d o not demonstrate whether the Metastatic breast cancer in the femur: A search for the lesion dependence of mechanical properties on density is altered at risk of fracture. Clin Orthop M3:282-288. by the presence of metastatic tumor. However, the data 7. Menck H, Schulze S. Larsen E 1988 Metastasis size in pathoshow that modulus is reduced by the presence of metastatic logic femoral fractures. Acta Orthop Scand 59: 15 1- 154. 8. McBroom RJ, Cheal EJ, Hayes WC 1988 Strength reductumor. tions from metastatic cortical defects in long bones. J Orthop Several studies have related bone density as measured by R a 6:369-378. QCT to physical measurements of density and strength and 9. Hipp JA, McBroom RJ, Cheal EJ. Hayes WC 1989 Strucfound reasonably good correlations.(”’ In this study, QCT tural consequences of endosteal metastatic lesions in long was not a good predictor of measured apparent density (all bones. J Orthop Res 7:828-837. specimens pooled) and was able to explain only 18% of the 10. Hipp JA, Edgerton BC, An K-N, Hayes WC 1990 Structural variance in strength measurements. The correlation coefficonsequences of transcortical holes in long bones loaded in cients for regressions between QCT and bone density are torsion. J Biomech 231261-1268. lower than have been reported in other studies. This lack 11. Hipp JA, Katz G, Hayes WC 1991 Local demineralization as of correlation may in part reflect the difficulty of precisely a model for bone strength reductions in lytic transcortical metastatic defects. Invest Radio1 M:934-938. locating the volume of a specific specimen from CT exami-
PROPERTIES OF TRABECULAR BONE WITH METASTASES 12. Fornasier VL, Hornc J G 1975 Metastases to the vertebral column. Cancer 36590-594. 13. Miller F, Whitehill R 1984 Carcinoma of the breast metastatic to the skeleton. Clin Orthop 184:121-127. 14. Krishnamurthy GT, Tubis M, Hiss J , Blahd W H 1977 Distribution pattern of metastatic bone disease. A need for total body skeletal image. JAMA 237:2504-2506. 15. Asdourian PL. Weidenbaum M, DeWald RL, Hammerberg KW, Ramsey RG 1990 The pattern of vertebral involvement in metastatic vertebral breast cancer. Clin Orthop 250:164169. 16. Gibson LJ 1988 Cancellous bone. In: Gibson LJ, Ashby MF ( 4 s . ) Cellular Solids. Pergamon Press, New York, pp. 316-331. 17. Rice JC, Cowin SC, Bowman J A 1988 On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21:155-168. 18. Goldstein SA 1987 The mechanical properties of trabecular bone: Dependence on anatomic location and function. J Biomech 20:1055-1061. 19. Mosekilde L 1990 Age-related loss of vertebral trabecular bone mass and structure- biomechanical consequences. In: Mow VC. Ratcliffe A, Woo SLY (eds.) Biomechanics of Diarthrodial Joints, Vol. l l . Springer-Verlag, New York, pp. 83-w. 20. Gibson LJ 1984 The mechanical behaviour of cancellous bone. MIT Department of Materials Science and Engineering publication no. R84-15, order no. 772. 21. Hayes WC, Piazza SJ, Zysset PK 1991 Biomechanics of fracture risk prediction of the hip and spine by quantitative computed tomography. Radiol Clin North Am 29(1):1-17. 22. Springfield DS 1982 Mechanisms of metastases. Clin Orthop 169:15-19. 23. Harrington KD 1988 Mechanisms of metastases. In: Harring-
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ton KD (ed.) Orthopaedic Management of Metastatic Bone Disease. C.V. Mosby, St. Louis, pp. 15-31. 24. Jaffe H L 1958 Tumors metastatic to the skeleton. In: Jaffe H L (ed.) Tumors and Tumorous Conditions of the Bones and Joints. Lea & Febiger. Philadelphia, pp. 589-618. 25. Hoaglin DC. Mosteller F. Tukey J 1983 Understanding robust and exploratory data analysis. New York, Wiley, 1983. 26. Huber PJ 1981 Robust statistics. New York, Wiley, 1981. 27. Wilner D 1982 Cancer metastases to bone. In: Wilner D (ed.) Radiology of Bone Tumors and Allied Disorders. W.B. Saunders, Philadelphia, pp. 364-371 I . 28. Carter DR, Hayes WC 1977 The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg [Am] 59:954-962. 29. McBroom RJ, Hayes WC. Edwards WT. Goldberg RP, White AA Ill 1985 Prediction of vertebral body compressive fracture using quantitative computer tomography. J Bone Joint Surg [Am] 67:1206-1214. 30. Van Kuijk C, Grashuis JL, Steenbeek JCM. Schutte HE, Trouerbach WT 1990 Evaluation of postprocessing dualenergy methods in quantitative computed tomography. Invest Radiol 25:882-889. Address reprint requests to:
John A . Hipp. Ph.D. Beth Israel Hospital, RM DA 779 330 Brookline Avenue Boston, MA 02215 Received for publication October 7, 1991;in revised form April 3. 1992; accepted April 22, 1992.
Mechanical Properties of Trabecular Bone Within and Adjacent to Osseous Metastases JOHN A. HIPP,' ANDREW E. ROSENBERG,' and WILSON C. HAYES'
ABSTRACT Despite radiographic and histologic evidence of trabecular bone density changes within and adjacent to osseous metastases, there currently exist no data to demonstrate whether these changes are important in predicting the risk of fracture. To determine if these density changes result in significant reductions in mechanical properties, trabecular bone specimens were prepared from lower thoracic and lumbar vertebrae from two cadavers with radiographic, gross, and histologic evidence of lytic and/or blastic osseous metastases. Each specimen was classified as normal, lytic, or blastic based on appearance in fine-grain radiographs of 8-9 mm thick coronal plane sections. Specimens were tested to failure in uniaxial compression, and tissue and apparent densities were measured. Mean tissue densities were within normal ranges. The mean apparent density for all specimens combined was within the normal range for human vertebrae, and the mean apparent density for radiographically normal (0.131 g/ml) and lytic (0.111 g/ml) specimens was less than the mean apparent density of blastic (0.182 g/ml) specimens (p < 0.02). The moduli of lytic and blastic specimens were less than for normal specimens (p < 0.025). The strength of lytic specimens was less than normal (p = 0.0571, but the strength of blastic specimens was not (p > 0.1). Apparent density explained significant fractions of the variations in both modulus (p < 0.001) and strength (p < 0.001). The data suggest that blastic changes associated with osseous metastases to trabecular bone disrupt the normal dependence of trabecular mechanical properties on apparent density, but lytic changes do not. These data also suggest that fracture risk predictors that utilize bone density to estimate stiffness or strength should adjust for the effects of metastases.
INTRODUCTION s THE SURVIVAL TIME for patients with cancer increases, the need to manage osseous metastases has become a
A
more frequent and important clinical problem. The advantages of prophylactic stabilization of osseous defects compared with the management of pathologic fractures include increased life expectancy, reduced pain, and faster return to mobility.(l.'j Predicting which osseous defects should be prophylactically stabilized remains problematic and has been addressed in several ~ l i n i c a l ' ~ -and ' ~ in vitro studies. ('-'01 However, reliable and comprehensive criteria for prophylactic stabilization have yet to be developed. As with most structures, the strength of a bone is a function of geometric variables, material properties, and func-
tional demands. Several studies have considered the significance of defects with regular geometries in models of cortical bone in which the bone was assumed to have homogeneous material properties.(n-lO1Two of these studies have further suggested the importance of density changes adjacent to cortical However, no studies have considered the mechanical properties of trabecular bone from within and around osseous metastatic defects. This is an important concern, since the spine is the most common site for osseous metastases from many primary tumors(1'-'41 and metastases to the spine almost always involve trabecular bone. ( 1 5 ) Although a substantial literature is available on the mechanical properties of normal and osteoporotic trabecular bone, (l6-IP1 no studies have specifically reported the me-
'Orthopaedic Biomechanics Laboratory, Department of Orthopaedic Surgery, Charles A. Dana Research Institute. Beth Israel Hospital and Harvard Medical School, Boston, Massachusetts. 'James Homer Wright Pathology Laboratories, Department of Pathology, Massachusetts General Hospital, Boston.
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chanical properties of bone compromised by metastatic disease. For normal trabecular bone, power-law relations between trabecular bone density and strength or stiffness~17~1n~10’ have been described. However, there is considerable scatter in the coefficients for these relationships. (’I1 For bone compromised by metastases, the relationship between bone density and strength may depend on the primary tumor from which the metastasis arose. A variety of mechanisms for the bone resorption and formation that occur with metastases from various primary tumors have been suggested. ( l l m ) The radiologic and histologic evidence of lytic and/or blastic changes to bone within and adjacent to osseous metastases[141leads to the hypothesis that the mechanical properties could be significantly altered and thus could be an important factor in predicting fracture risk. To address this question, our first objective was to determine if lytic and blastic changes to trabecular bone alter its mechanical properties. We also wished to determine if relationships between trabecular bone density and strength or stiffness are altered by metastatic involvement.
MATERIALS AND METHODS Lumbar and thoracic vertebrae were obtained from two donors with osseous metastases noted on the medical histories. One donor was a 78-year-old female, with the cause of death listed as lung cancer, breast cancer, and melanoma. The other donor was a 82-year-old female with the cause of death listed as breast cancer. Anteroposterior (AP) and mediolateral (ML) radiographs of the intact thoracolumbar spine were obtained and used to identify metastases. Biopsies were obtained from sites of metastases by passing a 2 mm coring tool through the pedicle into the tumor sites. Decalcified, hematoxylin- and eosin-stained sections were prepared from each biopsy and analyzed by an orthopedic pathologist. Quantitative computed tomographic (QCT) scans were obtained for vertebrae with radiographically evident metastases and for the adjacent vertebrae. Vertebrae were immersed in a saline bath during scanning. Scans were obtained with a GE9800 scanner using 3.0 mm thick slices, 5.0 mm table increments, and a pixel size of 0.59 mm. A dipotassium phosphate phantom was included in the scans to allow quantitative analysis of bone density. CT data were transferred to SUN workstations (SUN Microsysterns, Mountain View, CA) for analysis of bone density. Individual vertebrae were isolated and embedded in a fast-curing foam (LiteCast; Isocast Systems, Inc., Clackamas, OR) to facilitate sectioning into specimens for mechanical testing. Care was taken to maintain appropriate anatomic orientation. Two coronal slabs were obtained through the centrum of each vertebrae using a band saw. Each slab was 6-9 mm thick. The end plates were not included. The slabs were analyzed visually for the presence of discoloration and texture characteristic of the presence of tumor.‘”’ Each slab was then radiographed (Faxitron; Hewlett-Packard, McMinnville, OR) using fine-grain film (Kodak X-Omat TL; Eastman Kodal Co., Rochester, NY)
to localize density changes characteristic of metastatic involvement. Cubic specimens approximately 8 mm wide in each dimension were then cut from each slab using a lowspeed diamond wafering saw (Isomet; Beuhler, Ltd., Lakebluff, IL), again being careful to maintain anatomic orientation. Cubes were cut such that mineralized tissue was present throughout the cube. Cubes in which large regions were completely demineralized were not utilized for testing. As a result of this protocol, specimens were subject to two freeze-thaw cycles before mechanical testing. Specimens were thawed to prepare the cubes, frozen, and then thawed just before testing. Specimens were not embalmed and were tested fully hydrated at room temperature. The location of each cube was carefully marked on the radiograph of the parent slab, and the overall radiographic appearance of the cube relative to all other sites for that donor was recorded as normal, lytic, or blastic. Using the marked radiographs, the approximate location of each cube was determined in the transverse C T data. Using SUNVISION image-processing software (SUN Microsysterns, Mountain View, CA) and the dipotassium phosphate phantom, the average density (expressed as g/ml of dipotassium phosphate) was determined for each cube. A total of 134 cubes of trabecular bone were prepared, evaluated densitometrically, and tested mechanically. The dimensions of each cube were measured to the hundredth of a millimeter three times using digital calipers and the average values calculated. Cubes were mechanically tested in uniaxial compression between rigid platens using a servohydraulic materials testing system (model 1331; Instron Corp., Canton, MA, with Series 3200 controller; Interlaken Technology Corp., Eden Prairie, MN). Displacement was measured using an extensometer connected to the platens, thereby eliminating the need to adjust for system compliance. Strain was calculated by dividing the platen displacement by the initial height. Cubes were tested to 5% strain at a strain rate of 0.2 s-l. Specimens were tested along the craniocaudal axis. Stress and strain data were recorded for each test using a personal computerbased data acquisition system (Dell 386SX; Dell Computers, Austin, TX, with a Data Translation DT2801A; Data Translation, Marlboro, MA, and Labtech Notebook software; Laboratory Technologies, Wilmington, MA). From these data, the ultimate stress (o,lt) was recorded, and a linear regression was fit to the data from 0 . 3 to~ ~ ~ ~ 0.70,1t. This linear regression was used to calculate the 0.2% yield stress. Densities for each specimen were determined following mechanical testing. Nonmineralized tissue was removed from specimens by ultrasonic treatment in a 0.5% solution of sodium hypochlorite and rinsing with a water jet. These two steps were repeated several times until there was no visible evidence of nonmineralized tissues. Wet weight was determined after thorough degassing. Apparent density was determined as the wet weight divided by the sample volume (volume determined before testing). Bone tissue volume was calculated as the hydrated weight less the submerged weight. Tissue density was calculated as the hydrated tissue mass divided by the bone tissue volume. Tissue densities less than 1.6 were considered to represent in-
1167
PROPERTIES OF TRABECULAR BONE WITH METASTASES
FIG. 1. High-resolution radiograph of an 8 mm thick slice through the fourth lumbar vertebrae of a cadaveric specimen for which the cause of death was listed as breast cancer. The section is in the coronal plane.
complete removal of marrow contents and thus unreliable density measurements. These specimens were excluded from the remainder of the analysis. Statistical analysis of the data was completed using RS1 and RS/Explore software (BBN Software Products Corp., Cambridge, MA). One-way analysis of variance was used to determine if the radiographic appearance was a predictor of apparent density. The hypothesis that lytic and blastic changes alter mechanical properties was investigated by one-way analyses of variance of the effect of radiographic appearance on modulus or strength. The hypothesis that the relationships between density and mechanical properties were different for bone compromised by tumor was investigated by analysis of covariance of the effects of radiographic appearance and apparent density on mechanical properties. Linear regressions were used to determine how well QCT was able to predict density. In several instances, the one-way analysis of variance was completed using medians rather than means. When data are outlier prone and/ or the variances between groups are not equal, analysis using medians is the preferred method. i z s ) Moreover, the use of medians is a conservative approach since it is less sensitive and produces lower significance levels than when using means.c2s1In most cases, the bisquare method was used to determine regression equation coefficients, since it tends to estimate coefficients with less sensitivity to outliers in the data. This is also a conservative approach and is less likely to report statistical significance that does not actually exist.'z61
RESULTS Pathologic analysis of the biopsies demonstrated metastatic deposits consistent with spread from breast cancer in both donors. There was no evidence of pathologic fractuires or other deformities. A few areas of increased den-
TABLE1. DISTRIBUTION OF TRABECLJLAR BONECUBES WITHIN THE THREERADIOGRAPHIC APPEARANCE CATEGORIES
Donor
Normal
Lytic
Blastic
Total
HI01 1
45 19 64
14 37 51
12 7
71 63 134
H937 Both
19
sity were radiographically evident in AP and ML plane films of the intact spines in each individual. From visual observation of radiographs of the thick slabs cut from each vertebrae, the trabecular bone appeared generally mottled, with several areas of locally increased density (Fig. 1) and a few areas of obvious lysis. A periosteal bone response was noted in most slabs, and involvement of the pedicles was evident in two vertebrae. The qualitative classification of cubes into normal, lytic, or blastic was not always clear. Several cubes appeared to be of mixed pathology and partly normal. In these cases the cubes were classified toward the extreme (i.e., a partly blastic cube was classified as blastic). More cubes were classified as radiographically normal than specimens classified as lytic or blastic (Table 1). Because 26 cubes had measured tissue densities less than 1.6,these data were eliminated from further consideration since low tissue density was assumed to be due to incomplete removal of marrow and thus unreliable. There was no obvious relationship between excluded specimens and donor or radiographic appearance. After exluding unreliable density data, the tissue densities ranged from 1.61 to 2.69 g/ml (mean 1.95; standard deviation, SD, 0.20). There were six specimens with tissue densities greater than 2 g/ml, two of which were classified as radiographically normal; the remaining four were classified as lytic. Apparent density data for both donors spanned a wide range
HIPP ET AL.
1168
(0.038-0.465 g/ml), and the distribution of densities was heavily weighted toward the low-density range (mean = 0.130 g/ml, SD 0.062). The mean apparent densities for the two donors were significantly different, both for all cubes (0.154 versus 0.108 g/ml, p = 0.0065) and for only radiographically normal specimens (0.150 versus 0.0924 g/ml, p = 0.0012).Tissue density explained only 4.5% of the variation in apparent density (p = 0.027), based upon linear regression with a bisquare estimation procedure. Based on one-way analysis of variance, radiographic appearance explained only 4.4% of the variation in tissue densities (p = 0.095), and there were no significant differences between means of the radiographic appearance groups. Radiographic appearance explained slightly more (13.4%) of the variation in apparent density (p = 0.0005). The value of apparent densities for normal and lytic specimens (Fig. 2) were significantly less than for blastic specimens (p = 0.013 and 0.0007 for lytic and blastic specimens, respectively). All points that fell outside the 95% confidence intervals for each group had apparent densities greater than expected. Before mechanical testing, each of the three dimensions of the cubic specimens were measured three times. The mean standard deviation of these measurements was 0.06 mm. Almost all stress-strain curves had both a linear region before failure and a definite ultimate stress (Fig. 3). There was greater uncertainty in the definition of a peak load with some of the specimens that failed at very low loads. Overall, a significant linear relation between the yield stress and the ultimate stress was found (oyld = 0 . 9 3 9 ~ ~-10.022; ~ r' = 0.99). A moderate linear correlation was found between ultimate stress and modulus (oulr = 0.0126E + 0.388; r' = 0.68) and yield stress versus modulus (uyld = 0.0119E + 0.33; r' = 0.70). Analysis of covariance was used to test the hypothesis that the presence of tumor affected bone modulus. This test was done twice, first using linear regressions, and then using linear regression on the logarithms of the data. The first test indicated that both radiographic appearance and apparent density affected elastic modulus (p c 0.001 for radiographic appearance and 0.0048 for apparent density). The slope of linear regressions relating apparent density to modulus appeared to be strongly influenced by high-density specimens and was not statistically different between the radiographic appearance groups (Fig. 4). In addition. the correlation coefficients for these regressions were very low (rl = 0.086, 0.14, and 0.11 for normal, lytic, and blastic specimens, respectively). However, the average modulus for radiographically normal specimens was significantly higher than for lytic or blastic cubes (p = 0.0018 and O.ooO1, respectively; Fig. 5 ) . Average moduli for lytic specimens were not statistically different than for blastic specimens. To address the issue of whether a power law would explain relationships between density and modulus better than a linear one, we also completed an analysis of covariance using the logarithms of apparent density and modulus. Compared to the residuals from the linear regressions using untransformed data, the residuals from the regressions to log data were greater and not as randomly distributed. The regressions using log data explained even
0.30-
I!'
4J
c
O.lO'
al
$ 1
.~
0.00
LYtlC
NO-1
8l..tIC
Radiographic Appearance Group FIG. 2. Simultaneous comparison of apparent density between radiographic appearance groups. The small boxes show the mean apparent density for each radiographic appearance group, and the bars attached to each box show the standard deviations. These error bars overlap if the difference between two means is not significant at the 5 % level. Significant differences are determined using Bonferroni's simultaneous confidence intervals for all comparisons. The grand average for all specimens is shown by the horizontal line, and the error bounds for this average are shown by the dashed lines.
1 0
I
uodu1u.I
1
I4n.m
str...'
STRAIN FIG. 3. Compressive stress-strain curve for a radiographically normal specimen. The yield stress, ultimate stress, and linear regression line used to calculate modulus are labeled.
1169
PROPERTIES OF TRABECULAR BONE WITH METASTASES
200,
.. ..
c
rd ..
v
/
/. \
m 0.0
0.1
0.2
0.3
0.4
0.5
APPARENT DENSITY (g/ml) FIG. 4. Uniaxial compressive modulus as a function of apparent density, grouped by radiographic appearance. Radiographically normal specimens are represented by solid squares, lytic specimens by open circles, and blastic specimens by open triangles. The linear regressions to the data for each radiographic appearance group are also shown. A thin solid line is used for the normal specimens, a heavy double line for lytic specimens, and a dashed line for blastic specimens. The slopes of these regression lines are not statistically different at the 5% level.
less of the variation. Regressions using log data also demonstrated no significant difference in slope between the radiographic appearance groups. After adjusting for apparent density using analysis of covariance, there was little evidence that radiographic appearance affected maximum stress (p = 0.061). However. apparent density affected the maximum stress after adjusting for radiographic appearance (p < 0.001). As with modulus data, there were several extreme observations with abnormally high densities. Linear or power-law regressions of density versus strength data were no better than found for density versus modulus. There was no difference between the mean yield stress or maximum stress for normal versus lytic or blastic specimens. Analysis of covariance of the effect of radiographic appearance and apparent density on QCT density suggests little dependence of QCT density on radiographic appearance (p = 0.054), but a strong dependence of QCT density on apparent density (p < 0.001). As with other parameters, specimens with high densities appeared as outliers. Robust (bisquare) linear regression of QCT density as a function of apparent density suggest moderate linear relationships, and the slope of the line fit to the data for blastic specimens (494 mg/ml per g/ml) was significantly greater (p = 0.0002)than the slope for normal specimens (218 mg/ml per g/ml).
DISCUSSION
1151
100'
RADIOGRAPHIC APPEARANCE
FIG. 5. Mean modulus for normal, lytic, and blastic specimens. Standard deviations are shown by the error bars. Using simultaneous comparisons, the modulus of radiographically normal specimens was different from that for lytic (p = 0.0013) or blastic (p = 0.023) specimens.
Although limited in scope, these measurements demonstrate that significant reductions in mechanical properties can accompany invasion of trabecular bone by tumor cells. Our data do not demonstrate whether the relationship between density and mechanical properties is changed by the presence of tumor. As far as we are aware, these are the first experiments to report measurements of the mechanical properties of trabecular bone from within and adjacent to osseous metastases. This study had several limitations. Since trabecular bone specimens from only two individuals were tested, it is not clear whether other primary tumors, or other pathologic manifestations of breast or lung metastases, have comparable effects on trabecular bone. The extent of tumor involvement in our bone specimens was difficult to determine from radiographs. Overall, the radiographic appearance of most of the slabs cut from each vertebrae was consistent with the mixed lytic and blastic characteristics that have been reported for breast cancer."'] Good agreement between fine-grain radiographic analysis of 4 mm thick coronal sections through vertebral bodies and histologic analysis has been reported in other studies. (I2) Although radiographic appearance should agree with histologic analysis, it does not provide a quantitative measurement of the extent of tumor involvement in each tested trabecular bone specimen. This was the most significant shortcoming of this study. Other methods that would quantify the extent of tumor were considered. It was not practical to analyze bone adjacent to each cube histologically, because the processing required to cut cubic specimens from vertebral
1170
HIPP ET AL.
bodies destroyed any useful cellular detail. Thus, we had nation. In addition, a greater variation in fat content may to use qualitative and subjective estimates of tumor in- occur with metastatically compromised bone. With singlevolvement in each specimen. This was complicated by the energy QCT, a variable fat content would adversely affect presence of both lytic and blastic changes in each donor measurement of bone density.(a01Thus dual-energy QCI’ and the greater incidence of blastic specimens from one may be advantageous in future studies of this type. To better identify fracture risk predictors that account donor compared to the other. In cases of complete bone lysis, it was of course not possible to test tissue within that for trabecular bone density changes within and adjacent to region, but it was possible to say which specimens directly osseous metastases, changes in the relationship between bordered that region and investigate the hypothesis that density and mechanical properties should be quantified. bone juxtaposed to regions of tumor lysis would be me- Based upon this study, a conservative adjustment for the effects of blastic changes in trabecular bone might be to chanically compromised by tumor. Published equations relating mechanical properties to place a limit on the upper bound of trabecular density, density are not always consistent since both linear and perhaps using the average density from radiographically power-law regressions are reported and the coefficients of normal trabecular bone sites. In practice, this could be acthese regressions vary considerably. (’I1 These relationships complished using interactive array editors to lower the denmay depend on species, anatomic location, orientation, sity of radiographically blastic regions to the average denand the method by which apparent density is mea- sity of radiographically normal regions. This prevents the ~ u r e d . ( ~ ’It. ~is~thus ’ difficult to show whether the radio- increased density of blastic regions from inappropriately graphically normal specimens tested in this study had nor- raising structural predictors that are weighted by density. mal mechanical properties. The mean tissue density was ACKNOWLEDGMENTS within reported normal ranges, but the standard deviation in this measure was greater than has been reported for norThis study was supported by NIH Grant No. CAN21 1mal bone.”’1 It is not clear whether this is because tumor physically altered the bone tissue or whether specimens 05, Biomechanics of Metastatic Defects in Bone, and the were not thoroughly cleaned of marrow components. The Maurice E. Meuller Professorship in Biomechanics at Harmeasured apparent densities for cubes classified as radio- vard Medical School (Dr. Hayes). The contributions of graphically normal were slightly higher than has been re- Dheera Ananthakrishnan, Alexa Page, and Steve Piazza to ported for radiographically normal vertebrae from an the preparation and testing of bone specimens are grateelderly human population. I1s.’pl The distribution of appar- fully acknowledged. ent densities in each of the radiographic appearance groups (Fig. 2), demonstrates that all the points that fell outside REFERENCES the 95% confidence intervals had apparent densities greater than expected. This suggests that it is difficult to I . Habermann ET, Sachs R. Stern RE, Hirsh DM, Anderson assess osteoblastic changes in trabecular bone even from WJ 1982 The pathology and treatment of metastatic disease fine-detail in vitro radiographs. of the femur. Clin Orthop 169:70-82. Elastic modulus predicted the ultimate compressive 2. Sherry HS, Levy RN, Siffert RS 1982 Metastatic disease of strength of trabecular bone compromised by tumor as well bone in orthopedic surgery. Clin Orthop 169:44-52. (r’ = 0.68) as has been reported for other sites.(”’ The 3. Beals RK. Lawton GD. Snell WE 1971 Prophylactic internal slope of linear regressions between density and the meafixation of the femur in metastatic breast cancer. Cancer 28: 1350- 1354. sured mechanical parameters appeared to be strongly influ4. Fidler M 1981 Incidence of fracture of metastases in long enced by the presence of outliers with high densities. The bones. Acta Orthop Scand 52623-627. slopes of these regression lines for the different radio5 . Bunting R , Larnont-Havers W, Schweon D. K h a n A 1985 graphic appearance groups were not statistically different. Pathologic fracture risk in rehabilitation of patients with For our data. linear regressions of density versus modulus bony metastases. Clin Orthop 192222-227. explained more of the variation in the data than did 6 . Keene JS, Sellinger DS, McBeath AA, Engber WD 1986 power-law fits. Our data d o not demonstrate whether the Metastatic breast cancer in the femur: A search for the lesion dependence of mechanical properties on density is altered at risk of fracture. Clin Orthop M3:282-288. by the presence of metastatic tumor. However, the data 7. Menck H, Schulze S. Larsen E 1988 Metastasis size in pathoshow that modulus is reduced by the presence of metastatic logic femoral fractures. Acta Orthop Scand 59: 15 1- 154. 8. McBroom RJ, Cheal EJ, Hayes WC 1988 Strength reductumor. tions from metastatic cortical defects in long bones. J Orthop Several studies have related bone density as measured by R a 6:369-378. QCT to physical measurements of density and strength and 9. Hipp JA, McBroom RJ, Cheal EJ. Hayes WC 1989 Strucfound reasonably good correlations.(”’ In this study, QCT tural consequences of endosteal metastatic lesions in long was not a good predictor of measured apparent density (all bones. J Orthop Res 7:828-837. specimens pooled) and was able to explain only 18% of the 10. Hipp JA, Edgerton BC, An K-N, Hayes WC 1990 Structural variance in strength measurements. The correlation coefficonsequences of transcortical holes in long bones loaded in cients for regressions between QCT and bone density are torsion. J Biomech 231261-1268. lower than have been reported in other studies. This lack 11. Hipp JA, Katz G, Hayes WC 1991 Local demineralization as of correlation may in part reflect the difficulty of precisely a model for bone strength reductions in lytic transcortical metastatic defects. Invest Radio1 M:934-938. locating the volume of a specific specimen from CT exami-
PROPERTIES OF TRABECULAR BONE WITH METASTASES 12. Fornasier VL, Hornc J G 1975 Metastases to the vertebral column. Cancer 36590-594. 13. Miller F, Whitehill R 1984 Carcinoma of the breast metastatic to the skeleton. Clin Orthop 184:121-127. 14. Krishnamurthy GT, Tubis M, Hiss J , Blahd W H 1977 Distribution pattern of metastatic bone disease. A need for total body skeletal image. JAMA 237:2504-2506. 15. Asdourian PL. Weidenbaum M, DeWald RL, Hammerberg KW, Ramsey RG 1990 The pattern of vertebral involvement in metastatic vertebral breast cancer. Clin Orthop 250:164169. 16. Gibson LJ 1988 Cancellous bone. In: Gibson LJ, Ashby MF ( 4 s . ) Cellular Solids. Pergamon Press, New York, pp. 316-331. 17. Rice JC, Cowin SC, Bowman J A 1988 On the dependence of the elasticity and strength of cancellous bone on apparent density. J Biomech 21:155-168. 18. Goldstein SA 1987 The mechanical properties of trabecular bone: Dependence on anatomic location and function. J Biomech 20:1055-1061. 19. Mosekilde L 1990 Age-related loss of vertebral trabecular bone mass and structure- biomechanical consequences. In: Mow VC. Ratcliffe A, Woo SLY (eds.) Biomechanics of Diarthrodial Joints, Vol. l l . Springer-Verlag, New York, pp. 83-w. 20. Gibson LJ 1984 The mechanical behaviour of cancellous bone. MIT Department of Materials Science and Engineering publication no. R84-15, order no. 772. 21. Hayes WC, Piazza SJ, Zysset PK 1991 Biomechanics of fracture risk prediction of the hip and spine by quantitative computed tomography. Radiol Clin North Am 29(1):1-17. 22. Springfield DS 1982 Mechanisms of metastases. Clin Orthop 169:15-19. 23. Harrington KD 1988 Mechanisms of metastases. In: Harring-
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ton KD (ed.) Orthopaedic Management of Metastatic Bone Disease. C.V. Mosby, St. Louis, pp. 15-31. 24. Jaffe H L 1958 Tumors metastatic to the skeleton. In: Jaffe H L (ed.) Tumors and Tumorous Conditions of the Bones and Joints. Lea & Febiger. Philadelphia, pp. 589-618. 25. Hoaglin DC. Mosteller F. Tukey J 1983 Understanding robust and exploratory data analysis. New York, Wiley, 1983. 26. Huber PJ 1981 Robust statistics. New York, Wiley, 1981. 27. Wilner D 1982 Cancer metastases to bone. In: Wilner D (ed.) Radiology of Bone Tumors and Allied Disorders. W.B. Saunders, Philadelphia, pp. 364-371 I . 28. Carter DR, Hayes WC 1977 The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg [Am] 59:954-962. 29. McBroom RJ, Hayes WC. Edwards WT. Goldberg RP, White AA Ill 1985 Prediction of vertebral body compressive fracture using quantitative computer tomography. J Bone Joint Surg [Am] 67:1206-1214. 30. Van Kuijk C, Grashuis JL, Steenbeek JCM. Schutte HE, Trouerbach WT 1990 Evaluation of postprocessing dualenergy methods in quantitative computed tomography. Invest Radiol 25:882-889. Address reprint requests to:
John A . Hipp. Ph.D. Beth Israel Hospital, RM DA 779 330 Brookline Avenue Boston, MA 02215 Received for publication October 7, 1991;in revised form April 3. 1992; accepted April 22, 1992.
