Wolff’s Law, Bone Formation, Modeling and Remodeling

After nearly 25 years of work in skeletal anatomy, adaptation, and orthopaedics, Julius Wolff published his seminal 1892 work on bone ‘transformation’ (known today as bone remodeling and modeling). Wolff’s work and his general view of how a limb bone’s morphology develops has evolved into a nebulous concept known as “Wolff’s law”, which is essentially the observation that bone changes its external shape and internal (cancellous) architecture in response to stresses acting on it. Although the rationale for the existence of Wolff’s law has been challenged on many fronts (Bertram and Swartz, 1991; Cowin, 1997; Currey, 1997; Cowin, 2001), many contemporary investigators still subscribe to the idea that there is a “Wolff’s law” which states that bone models and remodels in response to the mechanical stresses it experiences, resulting in a minimal-weight structure that is adapted to its applied stresses.

For example, should a fracture of a weight-bearing long bone heal with an angulation, each step that the patient subsequently takes would result in a bending stress with compression on the concave side at the angulation and tension on the convex side. Rather than progressively weaken the bone structure at this site, such repeated mechanical stress results in a modeling and remodeling, with new bone growth on the concave side and bone resorption on the convex side. If the patient is young enough, the bone will ultimately grow straight. In control-system terms, the applied mechanical stress causes a growth response that negates the applied stress — a closed-loop negative-feedback control system.

Although there are some examples that suggest that bone adaptation is regulated by a Mechanostat-like mechanism, there are many other examples that are not consistent with this mechanism. Many authors have made relevant observations regarding the phenomena of bone modeling and remodeling. An orthopaedic surgeon named Harold Frost made the following salient points:

  1. Remodeling* is triggered not by principal stress but by “flexure” (now called “strains”)
  2. Repetitive dynamic loads on bone trigger remodeling; static loads do not.
  3. Dynamic flexure causes all affected bone surfaces to drift towards the concavity which arises during the act of dynamic flexure.

To define some basic terms of bone growth, below is a list of characteristics in the formation (osteogenesis), modeling and remodeling of bone.

Osteogenesis

  • Bone formed on or in soft tissue
  • Occurs during embryonic development, early stages of growth, and during healing
  • Two major subclassifications: intramembranous ossification and endochondral ossification
  • Intramembranous: bone formed on soft fibrous tissue
  • Endochondral: bone formed on cartilage
    • Osteoblasts derived from mesenchymal cells act independent of osteoclasts
    • Potential to create large amounts of bone

Modeling

  • Bone formed on/in existing bone tissue
  • Occurs by and activation-formation (A-F) or activation-resorption (A-R) sequence
  • Occurs during growth and healing, and minimally after skeletal maturity
  • Osteoblasts and osteoclasts act independently at different sites
  • Potential to create or resorb large amounts of bone
  • Changes shape, curvature, or cortical thickness of a bone

Remodeling*

  • Bone both resorbed and formed at the same site
  • Occurs by the activation-resorption-formation (A-R-F) sequence
  • Occurs via secondary osteon (Haversian system) formation
  • Occurs from growth through death.
  • The main normal physiologic mechanism for altering bone material organization and mass in adult skeleton
  • At best, leads to maintenance of bone; but with age it leads to net loss of bone (osteoporosis)

*Remodeling refers to the activation-resorption-formation (A-R-F) sequence of the basic multi-cellular unit (BMU) that forms either a secondary osteon (Haversian system) within cortical bone or hemi-osteon on surfaces such as trabecular struts in cancellous bone. Some skeletal biologists still prefer to use the term remodeling as a “catch-all” phrase that refers more generally to both modeling and remodeling. An example of this can be found in the work of Donald H. Enlow and his collaborators. This more general use of remodeling is also common parlance among orthopaedic surgeons. It is of historical interest that Harold Frost, the champion of the modeling-remodeling nomenclature used here, was an orthopaedic surgeon but he could not convince the vast majority of his colleagues to adopt his definitions.

Figure 1. These images above are diagrams showing bone that has been remodeled. “Remodeled” bone, by definition, is bone that has been reconstructed with secondary osteons (Haversian systems).

The image at the left shows about 30 secondary osteons per square millimeter.

The image at the right shows about 15 secondary osteons per square millimeter.

However, because of differences in osteon size, the percent remodeled bone is 50% in the left image and 70% in the right image.

  • On.N/T.Ar = number of secondary osteons per total image area (including pore spaces but not osteocyte lacunae). This is also known as OPD, or osteon population density (of secondary osteons of course!).
  • On.Ar/T.Ar = fractional area of secondary bone, or FASB. This is often expressed as a percentage (i.e., the value is multiplied by 100).
  • On.Ar = osteon area
  • On.Dm = osteon mean diameter in microns

References

Bertram JE, Swartz SM. 1991. The ‘law of bone transformation’: a case of crying Wolff? Biol Rev Camb Philos Soc 66:245-273.

Cowin SC. 1997. The false premise of Wolff’s law. In: Bone mechanics: CRC Press. p 30-31-15.

Cowin SC. 2001. The false premise in Wolff’s law. In: Cowin SC, editor. Bone Mechanics Handbook. Boca Raton, FL: CRC Press. p 30-31 – 30-15.

Currey JD. 1997. Was Wolff correct? Forma 12:263-266.