Stress-concentrating effect of resorption lacunae in trabecular bone

https://doi.org/10.1016/j.jbiomech.2004.12.027Get rights and content

Abstract

Analyses of the distributions of stress and strain within individual bone trabeculae have not yet been reported. In this study, four trabeculae were imaged and finite elements models were generated in an attempt to quantify the variability of stress/strain in real trabeculae. In three of these trabeculae, cavities were identified with depths comparable to values reported for resorption lacunae (∼50 μm)—although we cannot be certain, it is most probable that they are indeed resorption lacunae. A tensile load was applied to each trabeculum to simulate physiological loading and to ensure that bending was minimized. The force carried by each trabecula was calculated from this value using the average cross sectional area of each trabecula. The analyses predict that very high stresses (>100MPa) existed within bone trabecular tissue. Stress and strain distributions were highly heterogeneous in all cases, more so in trabeculae with the presumptive resorption lacunae where at least 30% of the tissue had a strain greater than 4000 με in all cases. Stresses were elevated at the pit of the lacunae, and peak stress concentrations were located in the longitudinal direction ahead of the lacunae. Given these high strains, we suggest that microdamage is inevitable around resorption lacunae in trabecular bone, and may cause the bone multicellular unit to proceed to resorb a packet of bone in the trabeculum rather than just resorb whatever localized area was initially targeted.

Introduction

Bone remodelling is a continuous process carried out by osteoclasts and osteoblasts in a coupled action of bone resorption and deposition. In trabecular bone osteoclasts travel along the surface of trabeculae, resorbing the tissue and forming a resorption cavity, and osteoblasts follow along behind filling in the cavity with osteoid, which subsequently mineralizes (Parfitt, 1984). It is generally agreed that this process tends to adapt the architecture of cancellous bone so that there is minimum stress in the bone tissue relative to its weight (Hart, 2001). However, it has been observed that microdamage is generated in both trabecular (Vashishth et al., 2000) and cortical bone (Lee et al., 2002) under everyday physiological loading conditions and these observations lead to the suggestion that trabecular bone remodelling may also prevent accumulation of microdamage, as has been hypothesised for compact bone (Carter et al., 1987; Frost, 1986; Martin and Burr, 1989; Prendergast and Taylor, 1994; Martin, 2002).

Because resorption cavities occurring during trabecular remodelling can be large relative to the size of the trabeculae, it is possible that significant elevations of stress occur around them. Van der Linden et al. (2001) constructed finite element models of cancellous bone at 28 μm resolution and resorption cavities were created by removing 28×28×28 μm3 volumes from the trabecular structures to create cavities 28, 56, or 84 μm deep. They observed that the presence of resorption lacunae resulted in increased strain at the base of the resorption cavity and decreased strain along the tip. However, given that resorption lacunae are typically 40–60 μm in depth, these resolutions could not give a detailed description of the consequences of resorption cavities on the strain distribution in bone tissue. For such an analysis models of individual trabeculae are required. Smit and Burger (2000) used finite element models of trabeculae assuming cylindrical geometry for the trabeculum and a hemi-spherical geometry for the Howship's lacuna on a trabecular surface. The trabeculum was loaded to produce 1000 microstrain in the longitudinal direction. They predicted increased strains both at the bottom of the lacuna and perpendicular to the direction of loading, where resorption is stopped and osteoblasts are recruited to fill the gap, and lower strains in the direction of loading, where osteoclast resorption activity continues. Based on these observations they proposed that BMU activity is regulated by strain, whereby low strains stimulate osteoclast resorption and increased strains inhibit osteoclasts and activate osteoblasts to refill. As the lacunar geometry was assumed hemi-spherical in their study, the analysis could not give information on the actual strains local to resorption cavities in vivo; such analyses would require finite element models with anatomically accurate trabecular bone geometries.

In this study, we hypothesise that bone resorption occurring during trabecular bone remodelling causes high stress concentrations in bone trabeculae. In particular we are interested to determine whether or not the stress concentrations could be of sufficient magnitude to generate damage in the bone tissue because, if it were, then damage around the resorption cavity could stimulate the continuation of the BMU activity and the travelling of a resorption pit across the trabecular surface.

Section snippets

Methods

Sections of cancellous bone from the proximal tibia, and the distal and proximal femur, of 6- and 10-month-old Whistar rats were cut under constant irrigation and were cleaned of bone marrow using a water jet. A dissecting microscope was used to locate trabecular rods, which were removed using a scalpel blade and forceps. Solid models of the microspecimens were generated using either serial sectioning and imaging at microresolutions, following the technique of Van der Linden (2002), or micro-CT

Results

The images obtained from serial sectioning were obtained at a resolution that was adequate for identifying the micro-structural geometry of trabeculae. Geometrical features such as the presumptive lacunae1 and side branching were observed in the cross-sectional images of some of the trabeculae [Fig. 4(a)].

The distributions of maximum principal stress

Discussion

In this study, we have shown that the stress/strain distribution within individual trabeculae is highly heterogeneous, even under the simplified loading conditions employed in our analysis. Furthermore it was predicted that stress and strain levels within trabeculae are elevated by the presence of what seem to be resorption lacunae. In each of the trabeculae the elevated stresses were associated with the locations of the cavities.

A number of assumptions were made in this analysis that require

Acknowledgements

Financial support provided by the European Commission Framework 6 program (Quality of Life and Management of Living Resources) project, “Mechanical Integrity and Architecture of Bone: Mechanical Integrity and Architecture of Bone Relative to Osteoporosis, Ageing and Drug Treatment (MIAB)”.

References (35)

  • G.C. Reilly

    Observations of microdamage around osteocyte lacunae in bone

    Journal of Biomechanics

    (2000)
  • J.Y. Rho et al.

    Elastic properties of human cortical and trabecular lamellar bone measured by nanoindentation

    Biomaterials

    (1997)
  • S.D. Ryan et al.

    Tensile testing of rodlike trabeculae excised from bovine femoral bone

    Journal of Biomechanics

    (1989)
  • B. Van Rietbergen et al.

    A new method to determine trabecular bone elastic properties and loading using micromechanical finite-element models

    Journal of Biomechanics

    (1995)
  • D. Vashishth et al.

    In vivo diffuse damage in human vertebral trabecular bone

    Bone

    (2000)
  • S. Vedi et al.

    The effects of long-term hormone replacement therapy on bone remodeling in postmenopausal women

    Bone

    (1996)
  • D.R. Carter et al.

    Fatigue behaviour of adult cortical bone: the influence of mean strain and strain rate

    Acta Orthopedica Scandinavica

    (1981)
  • Cited by (73)

    • Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling

      2021, Bone Remodeling Process: Mechanics, Biology, and Numerical Modeling
    • On the evolution and contemporary roles of bone remodeling

      2020, Marcus and Feldman’s Osteoporosis
    • Stress concentrations and bone microdamage: John Currey's contributions to understanding the initiation and arrest of cracks in bone

      2019, Bone
      Citation Excerpt :

      It also may be possible that pre-existing resorption pits can nucleate cracks at their base because of high stresses there [39–41], although there is some controversy about the relative importance of this to crack formation [42]. McNamara et al. [40] estimate stress concentration factors of about 3 at the base of the resorption cavity, which agrees quite well with Currey's estimate for a cylindrical pore at a right angle to the direction of stress. Many resorption pits tend not to be very circular (Fig. 8) (also see Fig. 9 in Ref. [43]) and stress concentrations at the tip of a cutting front can be several times larger than this.

    • Coupling of bone formation and resorption

      2019, Principles of Bone Biology
    View all citing articles on Scopus

    This paper was presented, in part, at the 13th Conference of the European Society of Biomechanics (ESB), Wrocław, Poland, in September 2002, where it won the ESB Student Award for best student presentation.

    View full text