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The Microstructure of Bone and Its Susceptibility to Fracture

Tony Keaveny, UC Berkeley

Andrew Burghardt, Glen Niebur, Jonathon Yuen, UC Berkeley

A s people age, their bones become more brittle and susceptible to breaks or fractures--a state that can be exacerbated by diseases that deteriorate bone tissue, such as osteoporosis. In this weakened state compressive stress injuries can seriously damage trabecular bone, the "spongy" type of bone found in the spine, hips, knees, and other joints. Designing drugs or other therapies to strengthen this tissue and determining the most effective strategies for early diagnosis and prevention, all require a detailed understanding of the structure of trabecular bone, its relationship to a bone's overall strength, and the way it reacts to compression.

Tony Keaveny, director of the Berkeley Orthopaedic Biomechanics Laboratory at UC Berkeley, and his group are attempting to gain such an understanding, but they must confront significant challenges arising from the nature of this porous bone. "Bone is a composite of minerals and collagen," Keaveny said, "and there are two types: trabecular, found in the spine and joints, and cortical, or compact, found in the mid-sections of long bones. We know more about the properties of cortical bone. It seems obvious to say that trabecular and cortical are made of the same material, but there's no reason why they'd have to be. Our research began with the assumption that they were indeed the same, and we're now pretty convinced that we were right."

Applying the properties of compact bone started Keaveny's group down the path toward the next challenge. "From that base point there are still significant differences from specimen to specimen," Keaveny said, "even when samples are taken from the same host and the same anatomical site" (Figure 1). Arriving at statistically reliable conclusions about how trabecular bone responds to compressive stress therefore requires hundreds of experiments. This either means acquiring hundreds of pieces of bone, or creating computer models upon which experiments can be conducted hundreds of times.





Discrepancy Across Bone Samples
Discrepancy Across Bone Samples
Figure 1. Discrepancy Across Bone Samples
Four samples of trabecular bone demonstrate how the architecture and density of the bone can vary both between and within anatomic sites, thus complicating investigation into how trabecular bone responds to compressive stress.


Data from bone scans would seem like a reasonable source for generating such models, but according to Glen Niebur--a Ph.D. student working with Keaveny--the best-quality clinical scans that can be obtained from living organisms are still have a resolution more than 100 microns, which may not capture enough detail to accurately model the bone in some regions.

In the interim, a computer-controlled milling machine grinds silver nitrate-stained samples into 20-micron slices that are then digitally photographed and reassembled as 3-D computer images composed of hundreds of thousands of voxels. Similarly high-quality images can also be obtained using micro-CT (Computed Tomography) scanners. To reduce the amount of time spent developing the finite-element model, typically the most labor-intensive part of finite element analysis, these voxels are directly converted to eight-node linear finite elements.

"There is one disadvantage to this," Niebur said. "Because of the voxel shape, the edges of our models are never smooth and we have slight numerical errors. On the other hand, the fact that all of the finite-elements are the same size and shape helps us in the solution process: We can run faster solution algorithms."

To save valuable compute time on the Cray T3E at SDSC, the model's resolution is often decreased before generating the finite-element model. Based on preliminary work, the group has determined a relationship between the image resolution and the bone architecture that limits the final solution errors to less than 5 percent.

Each run of an MPI-coded 5x5x5-mm finite-element model on the T3E consumes 180 processor hours, or about 12 wall-clock hours. "This is down from 280 processor hours," Niebur said. "Since the heterogeneity of
the bone requires us to run hundreds of simulations and supercomputing resources are limited, we're continually optimizing the code." The group has run 50 simulations so far this year and plans another 50 before the end of 1999.

"It wouldn't be possible to do what we're doing without supercomputing resources," Keaveny said. "And we don't see an end to the need for high-performance parallel computation."

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Results of Finite Element Simulations for a Sample of Bovine Tibial Trabecular Bone
Figure 2. Results of Finite Element Simulations for a Sample of Bovine Tibial Trabecular Bone
At right, simulations are loaded along the principal trabecular axis (vertically); at right, transverse to the principal axis (horizontally). The applied strain increases from top to bottom, with about three times as much tissue yield on-axis compression as for transverse compression. About half of the yielded hard tissue yields in tension for on-axis compression, and about two-thirds for transverse compression.


The group is now focusing on hip and spine fractures using models assembled from bovine and human cadaver bone samples. "Numerous theories have been proposed about how the microstructure of trabecular bone relates to the macrostructure," Niebur said. "We can test those theories by essentially taking one piece of bone and doing hundreds of experiments on it, varying the loading conditions in the model. What we learn about the structure and function on a small scale helps us better understand the tissue on a larger scale."

Though the group is focusing on the effects of compression, tension is also simulated, helping them to better understand the subtler biomechanical aspects. For example, it is well known that bone is weaker in tension than compression and, indeed, under tensile stress the majority of failure is due to tension. "But, under compressive stress, about one-third of the failure of the microstructural elements was predicted to be due to tensile stress, too," Keaveny said. "This was startling to observe" (Figure 2).

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It is also of great importance to those working on drugs and therapies for patients with degenerative bone disorders. "The type of the bone you have may be just as important as how much you have," Keaveny said. In a patient suffering from osteoporosis, for example, the pore walls, or struts, of the trabecular bone are in a state of deterioration.

"Such deterioration can make the bone more susceptible to tensile failure," he said. "The struts running horizontally, or perpendicular to the loading force, appear to fail by tension even though the whole piece of bone is loaded in compression." This helps explain why backs, hips, and other joints are commonly a source of trouble for older individuals.

"Diagnostics and treatments should take these results into account," Keaveny said. "At the least we should be assessing the effects of current drug therapies to make sure that they do not promote tensile failure mechanisms." Drugs that increase bone mass, for example, should not upset the delicate balance between the architecture of the bone and the way it fails. If they do, then added bone mass may not mean added strength.

At the same time as their work helps to advance progress in drug therapy, their current need for high-resolution data to feed finite-element models also pushes the boundaries of imaging research. The group recently received a grant from the National Institutes of Health to continue collaboration with researcher Sharmila Majumdar and her MRI group at UC San Francisco. "With continued advances in medical imaging coupled with this type of modeling," Keaveny said, "we will eventually be able to assess a person's bone strength non-invasively, with an accuracy comparable to direct mechanical testing." --AF *

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