Presented previously in part at the Proceedings of European Society of Biomechanics, Toulouse, France, July 10–14, 1997. Weinans H, Homminga J, Van Rietbergen B, Ruegseger P, Huiskes R 1998 Mechanical effects of a single resorption lacuna in trabecular bone. J. Biomech 31(Suppl 1):152.
The skeleton is continuously being renewed in the bone remodeling process. This prevents accumulation of damage and adapts the architecture to external loads. A side effect is a gradual decrease of bone mass, strength, and stiffness with age. We investigated the effects of bone loss on the load distribution and mechanical properties of cancellous bone using three-dimensional (3D) computer models. Several bone loss scenarios were simulated. Bone matrix was removed at locations of high strain, of low strain, and random throughout the architecture. Furthermore, resorption cavities and thinning of trabeculae were simulated. Removal of 7% of the bone mass at highly strained locations had deleterious effects on the mechanical properties, while up to 50% of the bone volume could be removed at locations of low strain. Thus, if remodeling would be initiated only at highly strained locations, where repair is likely needed, cancellous bone would be continuously at risk of fracture. Thinning of trabeculae resulted in relatively small decreases in stiffness; the same bone loss caused by resorption cavities caused large decreases in stiffness and high strain peaks at the bottom of the cavities. This explains that a reduction in the number and size of resorption cavities in antiresorptive drug treatment can result in large reductions in fracture risk, with small increases in bone mass. Strains in trabeculae surrounding a cavity increased by up to 1000 microstrains, which could lead to bone apposition. These results give insight in the mechanical effects of bone remodeling and resorption at trabecular level.
IT IS believed that the structure of cancellous bone adapts to external loads by modeling and remodeling processes, which result in an architecture well suited for its load-bearing function.(1–3) In the remodeling cycle, bone matrix is resorbed by osteoclasts, which make resorption cavities of 40–60 μm deep. In approximately 3 months, these cavities are refilled with new bone matrix by osteoblasts. The formation and resorption phase are coupled so that the bone mass stays approximately constant during this continuing process of physiological remodeling.(4) Nevertheless, after the age of 30 years, the bone mass decreases slowly with age because there is a small deficit of osteoblast formation relative to osteoclast resorption. Moreover, disconnected trabeculae are probably not repaired.(4) In general, the amount of bone loss with aging in the spine and hip is in the order of 0.5% of the bone volume per year. The increase in resorption depth and activation frequency(5,6) during menopause result in faster bone loss,(7) as trabeculae are disconnected and plates are perforated. The decrease of bone mineral content (BMC) or bone mineral density (BMD) is the most important reason for reduced load-bearing capacities of bone in elderly people.(8) However, the decrease in bone strength and increase in fracture risk cannot be explained fully by the decrease of BMC or BMD.(9) This has resulted in a considerable interest in the architecture of cancellous bone, which could further explain the changes in the quality of the bone and the complementary increase in fracture risk.
Developments in three-dimensional (3D) imaging have resulted in 3D quantification methods for the cancellous architecture.(10–13) These methods have been used to gain a better understanding of the mechanical functioning of cancellous bone and to find relationships between the morphological parameters and mechanical properties such as strength and stiffness.(14,15) However, small changes in the architecture, which cause small changes in the morphological parameters, can considerably change the load distribution and thereby have a potentially large effect on the mechanical properties and the fracture risk.(16) Bone remodeling causes changes in the architecture. After peak bone mass has been reached, bone is lost slowly; in the long term, trabeculae become thinner and plates are converted to rods. In the short term, resorption cavities are created. A resorption cavity with a depth of 40–60 μm can deteriorate considerably the properties of a trabecula with a thickness of approximately 100 μm. When a trabecula is loaded to failure and breaks, the loads in the surrounding trabeculae increase, resulting in potential failure of the structure. Insight into the strain distribution in trabeculae thus could be useful in understanding mechanical aspects of bone loss and remodeling in cancellous bone and in predicting fracture risk. Strains in trabecular bone cannot be measured experimentally in vivo, in contrast to strains in cortical bone.(17–21)
The purpose of our work was to quantify the strain distribution in the trabeculae of cancellous bone and to estimate the mechanical effects of bone loss and bone remodeling. Using computer models that incorporate the full 3D architecture of cancellous bone, we calculated the strains in individual trabeculae under normal physiological loading conditions. This enabled us to study how apparent level loading is resolved into tissue level deformations. Furthermore, we determined the changes in strain distribution and mechanical properties that resulted from bone loss by simulating various cases of bone loss in computer models. The results of these simulations show the mechanical effects of bone loss and remodeling at trabecular level.
MATERIALS AND METHODS
In this study we used cancellous bone specimens, which were microcomputed tomography (micro-CT) scanned or serially sectioned to obtain a 3D reconstruction of the cancellous bone architecture. A specimen of 6 × 6 × 6 mm from the proximal end of an autopsy human tibia was sectioned serially in slices of 20 μm and digitized.(22) The 3D architecture was reconstructed in a computer model by converting the voxels to elements of 60 × 60 × 60 μm.(23,24) The volume fraction of this specimen was 13.9%. Three specimens from the center of human vertebral bodies were reconstructed using a micro-CT scanner.(25,26) The donors were two males, of 37 and 77 years old (M37 and M77, respectively) and one female, 80 years old (F80). These data sets were coarsened to obtain finite element computer models of trabecular bone (4 × 4 × 4 mm) with brick elements of 28 × 28 × 28 μm. The volume fractions of these specimens were 7.4% (F80), 10% (M37), and 8.9% (M77). The tissue material properties in the computer models were chosen isotropic with a Young's modulus of 5000 MPa and a Poisson's ratio of 0.3.(24,27)
Using these finite element models, several computer simulation experiments were performed to investigate the effects of bone loss on the strain distribution within the trabeculae. If a cancellous architecture is well suited for its load-bearing function, then the load will be distributed equally over all elements in the structure, resulting in a narrow strain distribution.
Experiment 1: worst case and best case scenario of bone loss
The model of the cancellous bone specimen from the proximal tibia was loaded in the computer simulation in the superior-inferior (SI) direction, which corresponds to the in vivo loading axis. At the bottom face, displacements in the SI direction were constrained, a displacement of −1 mm in the SI direction was prescribed to the top face. Displacements in the side planes were suppressed for directions perpendicular to these planes. The strains in the trabeculae and the reaction force at the top surface were calculated using finite element analyses.(24) This reaction force was related linearly to the prescribed displacement and the Young's modulus of the cancellous bone tissue, because of the assumed linear elastic material properties. The strains were recalculated to correspond to a force of 18N, which equaled an apparent stress of 0.5 MPa. The maximal principal strains in the trabeculae were calculated. Changes in the maximal principal strain distribution because of bone loss were studied in three cases. First, a simulation of bone loss randomly distributed over the trabecular structure was performed. Second, bone was removed at locations of high strain; and third, bone was removed at locations of low strain. With these simulations, insight into the influence of the location of bone loss on the deterioration of the mechanical properties of cancellous bone was obtained.
Experiment 2: bone loss caused by bone remodeling
Although the previous simulation analyses may mimic potential stages of net bone loss, they certainly differ from the way in which bone is normally lost in vivo. The computer simulations in this second experiment mimicked both bone loss in resorption cavities, the direct effect of bone remodeling, and thinning of trabeculae, the long-term effect of remodeling with a formation deficit.
To simulate the direct effect, resorption cavities were created in the three models of vertebral cancellous bone, randomly distributed over the surface of the trabeculae. The depth of these resorption cavities was 56 μm, which is in the biologically relevant range.(28) In five steps, up to 20% of the bone volume was removed by creating resorption cavities (Table 1). To simulate long-term bone loss, trabeculae were thinned in five steps. In each step, more surface elements were removed from the trabeculae, until 20% of the bone volume was removed in the fifth step (Table 1). Thinning of trabeculae and creating of resorption cavities are illustrated in Fig. 1.
Table Table 1.. Volume Fraction in Five Steps of Bone Loss by Thinning of Trabeculae or by Resorption Cavities
A load of 8N was applied to the finite element models in the SI direction, which corresponds to the in vivo loading axis, as described in experiment 1. This load equaled an apparent stress of 0.5 MPa, which is in the physiologically relevant range.(29) The global stiffness matrix of the specimens was calculated in all phases of bone loss, by simulating three compressive and three shear tests in the finite element models. From this matrix, the Young's moduli of the specimens in the three principal orthogonal directions were determined, using an optimization procedure.(23) In addition, the strain distributions in the original model and after 20% bone loss caused by resorption cavities or by thinning of trabeculae were determined and compared.
Experiment 3: resorption cavities in detail
In this experiment, the effect of resorption cavities on the load distribution in the trabeculae was studied in more detail. One horizontal and one vertical trabecula were selected in the reconstruction of a vertebral body specimen (F80). Both trabeculae, located in the center of the reconstruction, had a rodlike shape and a diameter of approximately 120 μm. In the vertical trabecula, a resorption cavity was created. This cavity was made deeper gradually, until the trabecula was disconnected. In each step, the whole specimen was loaded in the SI direction with a force of 8N (0.5 MPa) in a finite element simulation, as described in experiment 1. The same experiment was performed in the horizontal trabecula. We investigated the changes in strain in the resorbed trabecula itself and the redistribution of the loads throughout the specimen that resulted from a resorption cavity in one trabecula.
Calculated strain distributions in trabecular bone specimens
A force of 18N (0.5 MPa) on the top surface of the tibial specimen resulted in an apparent strain of 0.36% (3600 microstrains). In 90% of the elements, the strain was lower than 700 microstrains; in most of these elements the strain was approximately 100 microstrains (Fig. 2). This equal distribution of the load over the elements indicates that this specimen is well suited for its load-bearing function in the SI direction. The same apparent stress applied to the vertebral specimen resulted in an apparent strain of 0.54% (5400 microstrains). In this specimen the strain in 90% of the elements was lower than 4300 microstrains, with most elements showing a strain of approximately 1000 microstrains (Fig. 3C). This wider strain distribution shows that the vertebral specimen had a lower stiffness and a less efficient architecture. In this specimen, the applied stress might cause microdamage in a mechanical experiment in which a stress of 0.5 MPa is applied to the specimen.(30) The average tissue strains were much lower than the apparent strain, because a lot of trabeculae bend as the whole specimen is compressed.
Worst case and best case scenario of bone loss
Randomly removing elements from the bone structure degraded the mechanical properties; the strain distribution flattened out significantly after removal of 25% of the bone volume. Up to 41% of the bone volume could be removed before the strain distribution became completely flat, indicating highly strained as well as almost unloaded elements in the structure (Fig. 2A). The deterioration of the trabecular architecture depended largely on the location of the bone loss. Bone matrix removed at locations of low strains had a minor effect on the distribution, as shown in Fig. 2B. Even after removal of 50% of the bone volume at locations of low strain, the distribution showed a narrow peak at 400 micro-strains and almost no increase in the number of highly strained elements was found. In contrast, removal of only 4% of the bone volume at locations of high strain caused a considerable change in the strain distribution and 7% loss resulted in a completely flattened strain distribution and a 10-fold increase of the average strain (Fig. 2C).
Bone loss caused by bone remodeling
The calculated stiffness of the three vertebral specimens is shown in Table 2. Figure 4 shows the distribution of the maximal principal strain over the trabeculae in 2 × 2 × 2 mm from the center of specimen F80. Resorption cavities caused a larger decrease in stiffness than thinning of trabeculae, especially in the SI direction. Removal of 20% of the bone volume by resorption cavities decreased the apparent stiffness in the SI direction by 50%, compared with a decrease of only 30% caused by thinning of trabeculae, as can be seen in Fig. 3A. The difference between the slopes of the regression lines was significant (p < 0.001). In transversal directions there was no significant difference between decrease in stiffness caused by thinning of trabeculae or resorption cavities, as can be seen in Fig. 3B.
Table Table 2.. Stiffness of the Three Vertebral Specimens Calculated Using Finite Element Simulations, SI, and Transversal Directions
The lower stiffness that results from resorption cavities is reflected in the strain distribution within the trabeculae. Resorption cavities resulted in a wider strain distribution and a lower peak at low strains, as can be seen in Fig. 3C.
Resorption cavities in detail
The vertical trabecula that was resorbed in this experiment functioned in its initial shape as a beam transferring compression and bending loads. The maximal strain in this trabecula was approximately 4000 microstrains (Fig. 5A). A small cavity as shown in Fig. 5B caused an increase in strain of approximately 1000 microstrains at the bottom of the cavity and a small decrease in strain near the rim of the cavity. These changes in strain are shown in Fig. 5G. With increasing resorption depth, the strain in the resorbed trabecula increased further. The neighboring trabeculae gradually took over the load, and the load transferred through the resorbed trabecula decreased. In the fifth step (Fig. 5E) extreme values, above 10,000 microstrains occurred in the resorbed trabecula. At this point, the load transferred through this trabecula was decreased by 25%. In step 6 (disconnection, Fig. 5F) the strains in the surrounding trabeculae were approximately 1000 microstrains higher than in the original configuration (Fig. 5H).
In the horizontal trabecula, the strain in the initial configuration was significantly lower; the maximum value was only slightly higher than 1000 microstrains. The resorption cavity in this trabecula had only minor effects; no extreme strain values were found. The strain in this trabecula doubled, and the load transferred through this trabecula decreased. The strain distribution in this trabecula with increasing resorption depth is shown in Fig. 6. In the third step, the load transferred through this trabecula was decreased by approximately 20%. However, because the load transferred through this trabecula was seven times smaller than the load transferred through the vertical trabecula, the strains in the neighboring trabeculae were almost unaffected. This difference between the effect of resorption cavities in the vertical and the horizontal trabecula is in agreement with the difference in decrease in stiffness between the SI and transversal directions caused by resorption cavities in the second experiment.
In the present study we have used computer simulation models to analyze how apparent level strains are resolved into local tissue level strains in trabecular bone specimens. Several bone loss scenarios were simulated to determine the changes in tissue level strains and mechanical properties. Although we have analyzed only a few specimens, we assume that these reveal some general concepts. We used specimens from male and female donors of different ages, and these samples showed similar results. The calculated tissue level strains were on average lower than the applied apparent strains and in the same range as experimentally measured strains in cortical bone.(21,31) This indicates that trabecular bone can deform heavily without high strains at the tissue level. Small amounts of bone loss at highly strained locations completely deteriorated the mechanical properties, while severe bone loss at locations of low strains (up to 50% of the bone volume) had only minor effects. This shows that cancellous bone has a large safety factor for bone loss, as long as the bone is not lost at highly strained locations. Resorption cavities caused large local increases in strain and a redistribution of the load over the trabeculae. The load transferred through the resorbed trabecula was decreased by up to 25%; the strains in the surrounding trabeculae were increased by up to 1000 microstrains. Combining these results, we can conclude that resorption cavities at locations of high strain would have an extremely deleterious effect on stiffness of trabecular bone.
The models used in this study represented accurately the 3D architecture of human cancellous bone; the level of refinement allowed accurate calculation of global mechanical properties and strain distributions using cubic brick elements.(23,24,32–34) Because we investigated small deformations, the behavior of the bone matrix could be considered linear. However, matrix properties at the microstructural level, such as microdamage and the lamellar structure of the bone matrix, were not incorporated in our models. Therefore, the present computer models are only suited to investigate the effect of architectural changes. A disadvantage of the use of cubic elements is the jagged representation of the surface of the trabeculae. This may cause errors in the interpolated stresses and strains at the surfaces. However, because most of the strains in the cross-sectional views are internal values and because we have not found extreme gradients in the strain values near the surfaces of the trabeculae, we do not feel that the errors caused by the jagged surfaces substantially affected our findings.
Recently, a technique was developed to determine strains in trabecular bone experimentally.(35) In this technique, X-rays or CT scans of trabecular bone specimens in loaded and unloaded situations are made and texture correlation is used to determine the strains in the trabeculae. The advantage of this method, compared with finite element models, is that no assumptions about the tissue mechanical properties have to be made. In contrast to texture correlation, in finite element simulations changes in the architecture can be studied easily, by changing the architecture in the model. The strain values found with these techniques cannot be compared directly, because different specimens were used. However, the output of both experiments is in the same range, and both techniques result in similar skewed strain distributions.
The finite element technique used in this study can be used to calculate strains in whole bones.(34) In the present study, we choose to calculate the strains in a smaller specimen, enabling the study of several bone loss scenarios within a reasonable amount of computing time. The strains found in the whole femur(34) were slightly lower than the strains found in the present study. This was probably caused by the cortical shell around the trabecular bone that was included in the whole bone model. This shell might enable a more homogeneous distribution of the load over the trabeculae, resulting in a narrower strain distribution and a lower average strain.
The question has been raised in the literature why the small increases in bone mass that result from bisphosphonate, calcitonin, or selective estrogen receptor modulator (SERM) treatment of osteoporotic patients result in reduced fracture risk at measurable levels.(36,37) This reduction in fracture risk could not be explained by the small increases in bone volume of 5–8% after 1–3 years alone.(38–40) Hence, it has been concluded that either the architecture improves considerably or the matrix tissue strength increases. Recently, the relation between the increase in BMD and the decrease in fracture risk was assessed using a compilation of data from a large number of studies.(41) A high correlation between increase in BMD and decrease in fracture risk was found. This supports the idea that the extra bone mass resulting from antiresorptive treatment is deposited where it is mostly needed, so that a small increase in bone mass can largely reduce fracture risk. From our first bone loss experiment it is clear that loss of 5% of the bone mass at highly strained locations can decrease the stiffness of the bone considerably. Furthermore, we showed that resorption cavities caused large decreases in stiffness and strain peaks at the bottom of the cavities. A decrease in the number of cavities would decrease the number of strain peaks; a decrease in depth of the cavities would decrease the strain at the bottom of the cavities. The known reduction in activation frequency and resorption depth that results from antiresorptive treatment(42) results in smaller cavities, which are more widely separated. This could result in a rather large increase in the stiffness and therefore also in strength(43) of the bone as can be concluded from the present finite element simulations.
Using the simulation results, we can gain insight into the influence of microdamage on bone remodeling. In cortical bone, it has been shown that damaged bone is remodeled preferentially.(44) Strain gauge experiments in animals and humans have shown strains in cortical bone up to 5000 microstrains under strenuous conditions.(21,31) From the calculated strain distributions in this study, we expect strains higher than 10,000 microstrains to occur in the trabeculae under these strenuous conditions. These strain values can cause damage in the bone matrix.(45) If remodeling is induced by microdamage, this remodeling process would start by resorption of the damaged tissue by osteoclasts. In the first experiment we showed that removal of 4% of the bone volume at highly strained locations, which are likely the locations where microdamage occurs, significantly deteriorated the structure. In normal physiology, approximately 15–20% of the trabecular bone is remodeled each year.(5) In combination with a duration of the remodeling cycle of 3–6 months, this yields that approximately 5% of the bone volume is undergoing remodeling at any time point.(28,46) Thus, it seems unlikely that osteoclasts resorb only damaged tissue. The cancellous bone structure would be at risk for failure continuously. Furthermore, the remodeling rate of the vertical trabeculae would be higher, because strains in vertical trabeculae under physiological loading are higher than strains in horizontal trabeculae, as shown in the present study. The formation deficit would result in thinning of the vertical trabeculae, with the horizontal trabeculae staying the same. In general, the opposite is found: the vertical trabeculae are conserved, while horizontal trabeculae are thinner, or even completely resorbed in old bone.(47)
Another topic of great interest is the coupling between osteoclast resorption and osteoblast formation. It has become clear recently that osteoblasts control osteoclast activity at the cellular level by receptor activator of NF-κB ligand (RANKL) and its decoy receptor osteoprotegerin,(48) but location-specific coupling remains to be explained. Recently, increases in strain at the bottom of a resorption cavity were shown in a simplified, cylindrical model of one trabecula.(49) If osteoblasts were activated by high strains, an automatic coupling would occur. In this study, we showed small increases in strain caused by a resorption cavity in a horizontal trabecula, in contrast to large increases in a vertical trabecula. A resorption cavity in a vertical trabecula also increased the strain in surrounding trabeculae (Fig. 5H). This could induce bone modeling and result in thickening of these surrounding trabeculae. This effect, apposition of bone matrix on trabeculae without previous resorption, has been shown in experimental studies.(50,51) This would decrease the load in the resorbed trabecula and slow down the bone formation in the cavity. Thick trabeculae would become thicker and thin trabeculae might completely disappear, which is in agreement with histological findings.(52) In real bone, numerous resorption cavities play a role, leading to an increased complexity in the dynamics.(53) Insight into this phenomenon could be obtained from finite element analyses in which bone remodeling is simulated as a dynamic feedback system.(54,55)
In conclusion, this study provides insight in the mechanical consequences of the bone remodeling process. This remodeling process, which is needed to maintain the trabecular architecture and to prevent the accumulation of damage, results in bone loss after peak bone mass has been reached. We have shown that the location of bone loss largely determines the mechanical consequences. From this we conclude that not all remodeling can be initiated at locations of high strains, the structure would be at risk for failure if all highly strained bone matrix was resorbed at the same time. These results support the idea that nontargeted remodeling, for example, calcium-homeostasis,(56) plays a role in the remodeling process. The large reduction in fracture risk that results from a small increase in bone mass in antiresorptive treatment can be understood from the strain increase caused by resorption cavities. Deep resorption cavities cause extremely high strains in the resorbed trabeculae. These large local increases in strain can explain the location-specific coupling between resorption and formation in the remodeling process. In addition, the altered strain distribution in the environment of a resorption cavity may trigger osteoblast activity in surrounding trabeculae. The known decrease in osteoclast activity and cavity size that results from antiresorptive treatment(42) will result in a drastic decrease of the strains at the bottom of the cavities and a large increase in the stiffness of the bone. In this study, we have shown that knowledge of the strain distribution at tissue level can help to explain the complex dynamics and mechanical effects of the bone remodeling process.
The micro-CT scans of the vertebral specimens used in this study were kindly provided by P. Ruegsegger and were obtained as part of the European Union Biomed 1 project “Assessment of bone quality in osteoporosis.”(26) J.C. van der Linden was supported by the Dutch Foundation for Research (NWO/MW); the research of H. Weinans was made possible by a fellowship from the Royal Dutch Academy of Sciences (KNAW).