A Contact Algorithm for Density-Based Load Estimation

Bone is a dynamic structure capable of adapting its shape and architecture to carry consistently applied loads with a minimum amount of material. As a result, the density distribution within bone contains direct information about these loads. In the following dissertation the linear density-based load estimation method was implemented and applied to two-dimensional coronal slices of the proximal femora of a chimpanzee, gorilla, grizzly bear and lion. In order to maintain the three-dimensional characteristics in the two-dimensional models, a back-plate was added to the diaphysis of each femora. A parametric study was performed on the back-plate to identify the effects of various parameters on the overall solution. As a result of this study, a simple method based on the geometry of bone is proposed for selecting the back-plate parameters. The results of the linear analysis indicated that the magnitude-weighted load directions may correlate to different modes of locomotion. However, There are limitations to the linear method. The linear method relies on assumed pressure distributions, which do not necessarily represent in-vivo pressure distributions. To address this issue, a contact algorithm was developed to model the interaction between the acetabular cup and femoral head. This not only produces physiological pressure distributions on the femoral head, but it also allows the pressure distributions to be associated with specific relative positions of the pelvis and femur, both of which are impossible using the linear method. Trends in the magnitude-weighted load direction from the contact algorithm are similar to the results from the linear method. Forward remodeling simulations illustrate that the loads determined from the contact algorithm and linear method are capable of producing key aspects of the density patterns found in the metaphysis of the femora. When compared to the results of the linear analysis, the density distributions from the contact algorithm better match the actual density distributions in the case of the lion and grizzly.

Year	Entry
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.
1985	Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.
1986	Hodge WA, Fijan RS, Carlson KL, Burgess RG, Harris WH, Mann RW. Contact pressures in the human hip joint measured in vivo. Proc Natl Acad Sci USA. May 1986;83(9):2879-2883.
1990	Fyhrie DP, Carter DR. Femoral head apparent density distribution predicted from bone stresses. J Biomech. 1990;23(1):1-10.
1976	Hegedus DH, Cowin SC. Bone remodeling: small strain adaptive elasticity. J Elast. October 1976;6(4):337-352.
1998	Martin RB, Burr DB, Sharkey NA. Skeletal Tissue Mechanics. New York, NY: Springer-Verlag; 1998.
1987	Carter DR, Fyhrie DP, Whalen RT. Trabecular bone density and loading history: regulation of connective tissue biology by mechanical energy. J Biomech. 1987;20(8):785-794.
1983	Frost HM. Bone histomorphometry: analysis of trabecular bone dynamics. In: Recker RR, ed. Bone Histomorphometry: Techniques and Interpretation. Boca Raton, FL: Inc., CRC Press; 1983:109-131.
1977	Carter DR, Hayes WC. The compressive behavior of bone as a two-phase porous structure. J Bone Joint Surg. 1977;59A(7):954-962.
2001	Garcia JM, Martínez MA, Doblaré M. An anisotropic internal-external bone adaptation model based on a combination of CAO and continuum damage mechanics technologies. Comput Methods Biomech Biomed Eng. 2001;4(4):355-377.
1987	Roesler H. The history of some fundamental concepts in bone biomechanics. J Biomech. 1987;20(11-12):1025-1034.
2000	Huiskes R. If bone is the answer, then what is the question? J Anat. August 2000;197(2):145-156.
1981	Roesler H. Some historical remarks on the theory of cancellous bone structure (Wolff's Law). In: Cowin SC, ed. Mechanical Properties of Bone. The Joint ASME-ASCE Applied Mechnics, Fluids Engineering and Bioengineering Conference; June 22-24, 1981; Boulder, CO. New York, NY: American Society of Mechical Engineers; 1981:27-42.
1994	Prendergast P, Taylor D. Prediction of bone adaptation using damage accumulation. J Biomech. August 1994;27(8):1067-1076.
1976	Cowin SC, Hegedus DH. Bone remodeling, I: theory of adaptive elasticity. J Elast. 1976;6(3):313-326.
1987	Afoke NY, Byers PD, Hutton WC. Contact pressures in the human hip joint. J Bone Joint Surg. August 1987;69B(4):536-541.
1989	Carter DR, Orr TE, Fyhrie DP. Relationships between loading history and femoral cancellous bone architecture. J Biomech. 1989;22(3):231-244.
1988	Whalen RT, Carter DR, Steele CR. Influence of physical activity on the regulation of bone density. J Biomech. 1988;21(10):825-837.
1985	Cowin SC, Hart RT, Balser JR, Kohn DH. Functional adaptation in long bones: establishing in vivo values for surface remodeling rate coefficients. J Biomech. 1985;18(9):665-684.
1986	Fyhrie DP, Carter DR. A unifying principle relating stress to trabecular bone morphology. J Orthop Res. 1986;4(3):304-317.
1992	Weinans H, Huiskes R, Grootenboer HJ. The behavior of adaptive bone-remodeling simulation models. J Biomech. December 1992;25(12):1425-1441.
2001	Hazelwood SJ, Martin RB, Rashid MM, Rodrigo JJ. A mechanistic model for internal bone remodeling exhibits different dynamic responses in disuse and overload. J Biomech. March 2001;34(3):299-308.
1987	Carter DR, Orr TE, Fyhrie DP, Schurmant DJ. Influences of mechanical stress on prenatal and postnatal skeletal development. Clin Orthop Relat Res. June 1987;219:237-250.
1990	Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling—application: a preliminary remodeling simulation. J Orthop Res. September 1990;8(5):662-670.
1987	Cowin SC. Bone remodeling of diaphyseal surfaces by torsional loads: theoretical predictions. J Biomech. 1987;20(11-12):1111-1120.
1987	Huiskes R, Weinans H, Grootenboer HJ, Dalstra M, Fudala B, Slooff TJ. Adaptive bone-remodeling theory applied to prosthetic-design analysis. J Biomech. 1987;20(11-12):1135-1150.
2001	Doblaré M, Garcia JM. Application of an anisotropic bone-remodelling model based on a damage-repair theory to the analysis of the proximal femur before and after total hip replacement. J Biomech. September 2001;34(9):1157-1170.
1994	Fischer KJ. Correspondence Between Bone Density Distributions and Mechanical Loading [PhD thesis]. Stanford University; December 1994.
1994	Mullender MG, Huiskes R, Weinans H. A physiological approach to the simulation of bone remodeling as a self-organizational control process. J Biomech. November 1994;27(11):1389-1394.
1995	Mullender MG, Huiskes R. Proposal for the regulatory mechanism of Wolff's law. J Orthop Res. July 1995;13(4):503-512.

Year

Entry

1990

Beaupré GS, Orr TE, Carter DR. An approach for time‐dependent bone modeling and remodeling: theoretical development. J Orthop Res. September 1990;8(5):651-661.

1985

Gibson LJ. The mechanical behaviour of cancellous bone. J Biomech. 1985;18(5):317-328.

1986

Hodge WA, Fijan RS, Carlson KL, Burgess RG, Harris WH, Mann RW. Contact pressures in the human hip joint measured in vivo. Proc Natl Acad Sci USA. May 1986;83(9):2879-2883.

1990

Fyhrie DP, Carter DR. Femoral head apparent density distribution predicted from bone stresses. J Biomech. 1990;23(1):1-10.

1976

Hegedus DH, Cowin SC. Bone remodeling: small strain adaptive elasticity. J Elast. October 1976;6(4):337-352.