In 1892, Julius Wolff published his seminal monograph on bone “remodeling” (transformation),* or the observation that the external shape and/or internal cancellous architecture of a bone can change in response to stresses acting on it. Based on observations, assumptions, predictions, and personal tenacity, Wolff’s general ideas have become known as “Wolff’s law” of bone adaptation. Although considered a “law,” this concept actually represents a broad set of hypotheses and observations, many of which are loosely connected and require rigorous investigation (see Bertram and Swartz, 1991; Biewener et al., 1997; Currey, 1997; Cowin, 1997). In fact, Wolff’s “law” is so broad reaching and nebulous that it evades rigorous description.

In a strict sense, Wolff’s “law” is synonymous with The Trajectorial Theory of Cancellous Bone Architecture. This is because Wolff placed heavy emphasis on transformation of cancellous bone architecture of various bones when viewed in thin sections or in roentgenograms. In this context, Wolff’s law states that trabeculae of cancellous bone form (during normal development or healing) with respect to stress trajectories produced by habitual mechanical loading. This ultimately results in an anatomical structure that is well suited, or adapted, to applied stress. The intellectual tradition of Wolff’s “law” can be traced to the early work of the notable Swiss engineer Carl Culmann — see Culmann’s cantilever and crane.

In 1973, Lance Lanyon published a paper in the Journal of Biomechanics reporting strain data on the calcaneus of adult sheep. In 1974 he wrote a manuscript published in the British Journal of Bone and Joint Surgery entitled the Experimental Support for the Trajectorial Theory of Bone Structure — Wolff’s law! Using stacked rosette strain gauges attached to sheep calcanei, Lanyon showed that the orthogonal in vivo principal strain trajectories were generally aligned with the predominant trabecular tracts. These studies have strongly influenced our work on the artiodactyl calcaneus as a “natural trajectorial structure.” and a structural and material model for interpreting bone adaptation (See our acoustic paper, our cement line paper, and additional work on the Trajectorial Theory including: Biewener et al., 1997, Cowin, 1997, Skedros and Brady, 2001).

In 1988 Dr. Skedros joined the Bone and Joint Research Laboratory under the direction of Roy D. Bloebaum, Ph.D. Dr. Bloebaum who had become the new director in the Fall of 1987. Dr. Skedros worked as a research fellow for one year between his junior and senior years of medical school at the University of Utah. At that time Dr. Bloebaum was interested in mineralization changes that might occur around femoral stem of total hip replacements. He theorized that there would be differences between the “tension” and “compression” sides of the femoral neck and proximal shaft, and that these would change as a result of alterations in stresses caused by the presence of the prosthesis. Consistent with conventional views, the “tension” side of the femoral neck is considered to the cranial or superior aspect, and the “compression” side is the caudal or inferior aspect. Dr. Bloebaum was pioneering the use of backscattered electron imaging in evaluating the interface between orthopaedic implants and bone. Dr. Skedros was assigned projects related to developing backscattered electron imaging technology, which could be used to quantify relative changes in mineralization at the microscopic level (e.g., within osteons and cement lines, or in larger areas containing many osteons, etc).

Teambone’s use of the artiodactyl calcaneus model resulted from a meeting that Dr. Skedros had with his mentor Dr. Dennis Bramble of the University of Utah Dept. of Biology. Dr. Skedros sought consultation with Dr. Bramble. Dr. Skedros described Dr. Bloebaum’s interest in quantifying relative mineralization changes between the tension and compression cortices of the femoral neck. Dr. Bramble thought that the habitual loading of the human femoral neck was too complex to be conceived as a simply loaded “tension/compression” bone. Dr. Bramble suggested that the use of the artiodactyl calcaneus might be more useful since it is simply loaded. Dr. Bramble’s graduate student, Russel Howard, had preliminarly data showing large mineral content differences between the cranial (“compression”) and caudal (“tension”) cortices of a small sample of antelope calcanei. Having read Lanyon’s 1974 paper just a few weeks before, Dr. Skedros then realized that the artiodactyl calcaneus could be historically linked to Wolff’s law — it was a natural paradigm of Culmann’s cantilever.

In November of 1988, another paper was published that strongly influenced our work. This was C. Owen Lovejoy’s The Evolution of Human Walking. This article profoundly influenced teambone’s work on Wolff’s trajectorial hypothesis.
*Note: It is unfortunate that the term remodeling is often used in this context since in modern parlance this term describes the process of osteon formation (see “Modeling/Remodeling”). The more appropriate term would be mini-modeling of the trabeculae (see the appendix of our trajectorial hypothesis paper).


Bertram, J. E. and Swartz, S. M., 1991. The ‘law of bone transformation’: a case of crying Wolff? Biol Rev Camb Philos Soc. 66, 245-273.

Biewener, A. A., Fazzalari, N. L., Konieczynski, D. D. and Baudinette, R. V., 1996. Adaptive changes in trabecular architecture in relation to functional strain patterns and disuse. Bone. 19, 1-8.

Cowin, S. C., 1997. The false premise of Wolff’s law. Forma. 12, 247-262.

Cowin, S. C., 2001. The false premise in Wolff’s law, in: Cowin, S. C., editor, Bone Mechanics Handbook, CRC Press, Boca Raton, FL, 30-1 – 30-15.

Currey, J. D., 1997. Was Wolff correct? Forma. 12, 263-266.

Lanyon, L. D., 1973. Analysis of surface bone strain in the calcaneus of sheep during normal locomotion. J Biomech. 6, 41-49.

Lanyon, L. E., 1974. Experimental support for the trajectorial theory of bone structure. J Bone Joint Surg. 56-B, 160-166.

Lee, T. C. and Taylor, D., 1999. Bone remodeling: Should we cry Wolff? Ir J Med Sc. 168, 102-105.

Lovejoy, C. O., Heiple, K. G., Meindl, R. S., Ohman, J. C. and White, T. D., 2002. The Maka femur and its bearing on the antiquity of human walking: applying contemporary concepts of morphogenesis to the human fossil record. Amer J of Phys Anthro. 119, 97-133.

Lovejoy, C.O. 1988. The Evolution of Human Walking. Sci American, Nov. 118-125.

Pontzer, H., Lieberman, D. E., Momin, E., Devlin, M. J., Polk, J. D., Hallgrimsson, B. and Cooper, D. M., 2006. Trabecular bone in the bird knee responds with high sensitivity to changes in load orientation. J Exp Biol. 209, 57-65.

Skedros, J.G. and Baucom S.L., 2007. Mathematical analysis of trabecular ‘trajectories’ in apparent trajectorial structures: The unfortunate historical emphasis on the human proximal femur. J. Theoretical Biology 244:15-45.