Finite Element Analyses of Fracture Healing in Long Bones

A general theory for the role of intermittently imposed stresses in the differentiation of mesenchymal tissue is presented and then applied to the process of fracture healing. Two- and three-dimensional finite element models of a healing osteotomy in a long bone were generated and the stress distributions were calculated throughout incremental stages of healing under various loading conditions. These calculations were used in formulating theoretical predictions of tissue differentiation that were consistent with the biochemical and morphological observations of previous investigators. Thus, the progressive ossification process in the fracture callus in a long bone was emulated. Specifically, the analyses could be used to predict the zones of initial ossification, periosteal bone deposition, bone bridging, and finally bone consolidation. The results suggest that intermittent hydrostatic (dilatational) stresses may play an important role in influencing revascularization and tissue differentiation and determining the histomorphological patterns of fracture healing.

Year	Entry
1970	Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.
1917	Koch JC. The laws of bone architecture. Am J Anat. March 1917;21(2):177-298.
1892	Wolff J. Das Gesetz der Transformation der Knochen. Berlin: Hirschwald; 1892.
1981	Carter DR, Vasu R, Spengler DM, Dueland RT. Stress fields in the unplated and plated canine femur calculated from in vivo strain measurements. J Biomech. 1981;14(1):63-70.
1966	Swanson SAV, Freeman MAR. Is bone hydraulically strengthened? Med Biol Eng. September 1966;4(5):433-438.
1988	Carter DR, Wong M. Mechanical stresses and endochondral ossification in the chondroepiphysis. J Orthop Res. January 1988;6(1):148-154.
1979	Perren SM. Physical and biological aspects of fracture healing with special reference to internal fixation. Clin Orthop Relat Res. January–February 1979;138:175-196.
1972	Rybicki EF, Simonen FA, Weis EB Jr. On the mathematical analysis of stress in the human femur. J Biomech. March 1972;5(2):203-215.
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.
1974	Reilly DT, Burstein AH. The mechanical properties of cortical bone. J Bone Joint Surg. 1974;56A(5):1001-1022.
1978	McKibbin B. The biology of fracture healing in long bones. J Bone Joint Surg. May 1978;60B(2):150-162.
1975	Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.
1984	Mow VC, Holmes MH, Lai WM. Fluid transport and mechanical properties of articular cartilage: a review. J Biomech. 1984;17(5):377-394.
1976	Hori RY, Mockros LF. Indentation tests of human articular cartilage. J Biomech. 1976;9(4):259-268.
1988	Carter DR, Wong M. The role of mechanical loading histories in the development of diarthrodial joints. J Orthop Res. 1988;6(6):804-816.
1984	Rubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads. J Bone Joint Surg. March 1984;66A(3):397-402.
1980	Carter DR, Smith DJ, Spengler DM, Daly CH, Frankel VH. Measurement and analysis of in vivo bone strains on the canine radius and ulna. J Biomech. 1980;13(1):27-38.
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.
1978	Hayes WC, Bodine AJ. Flow-independent viscoelastic properties of articular cartilage matrix. J Biomech. 1978;11(8-9):407-419.
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.
1985	Goodship AE, Kenwright J. The influence of induced micromovement upon the healing of experimental tibial fractures. J Bone Joint Surg. 1985;67B(4):650-655.
1981	Hayes WC, Snyder B. Toward a quantitative formulation of Wolff's Law in trabecular bone. 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; 1981:43-68.
1978	Carter DR, Spengler DM. Mechanical properties and composition of cortical bone. Clin Orthop Relat Res. September 1978;135:192-217.
1983	Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech. 1983;16(6):385-409.

Year

Entry

1970

Yamada H. Strength of Biological Materials. Evans FG, ed. Baltimore, MD: Williams & Wilkins Company; 1970.

1917

Koch JC. The laws of bone architecture. Am J Anat. March 1917;21(2):177-298.

1892

Wolff J. Das Gesetz der Transformation der Knochen. Berlin: Hirschwald; 1892.

1981

Carter DR, Vasu R, Spengler DM, Dueland RT. Stress fields in the unplated and plated canine femur calculated from in vivo strain measurements. J Biomech. 1981;14(1):63-70.

1966

Swanson SAV, Freeman MAR. Is bone hydraulically strengthened? Med Biol Eng. September 1966;4(5):433-438.

1988

Carter DR, Wong M. Mechanical stresses and endochondral ossification in the chondroepiphysis. J Orthop Res. January 1988;6(1):148-154.

1979

Perren SM. Physical and biological aspects of fracture healing with special reference to internal fixation. Clin Orthop Relat Res. January–February 1979;138:175-196.

1972

Rybicki EF, Simonen FA, Weis EB Jr. On the mathematical analysis of stress in the human femur. J Biomech. March 1972;5(2):203-215.

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.

1974

Reilly DT, Burstein AH. The mechanical properties of cortical bone. J Bone Joint Surg. 1974;56A(5):1001-1022.

1978

McKibbin B. The biology of fracture healing in long bones. J Bone Joint Surg. May 1978;60B(2):150-162.

1975

Reilly DT, Burstein AH. The elastic and ultimate properties of compact bone tissue. J Biomech. 1975;8(6):393-405.

1984

Mow VC, Holmes MH, Lai WM. Fluid transport and mechanical properties of articular cartilage: a review. J Biomech. 1984;17(5):377-394.

1976

Hori RY, Mockros LF. Indentation tests of human articular cartilage. J Biomech. 1976;9(4):259-268.

1988

Carter DR, Wong M. The role of mechanical loading histories in the development of diarthrodial joints. J Orthop Res. 1988;6(6):804-816.

1984

Rubin CT, Lanyon LE. Regulation of bone formation by applied dynamic loads. J Bone Joint Surg. March 1984;66A(3):397-402.

1980

Carter DR, Smith DJ, Spengler DM, Daly CH, Frankel VH. Measurement and analysis of in vivo bone strains on the canine radius and ulna. J Biomech. 1980;13(1):27-38.

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.

1978

Hayes WC, Bodine AJ. Flow-independent viscoelastic properties of articular cartilage matrix. J Biomech. 1978;11(8-9):407-419.

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.

1985

Goodship AE, Kenwright J. The influence of induced micromovement upon the healing of experimental tibial fractures. J Bone Joint Surg. 1985;67B(4):650-655.

1981

Hayes WC, Snyder B. Toward a quantitative formulation of Wolff's Law in trabecular bone. 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; 1981:43-68.

1978

Carter DR, Spengler DM. Mechanical properties and composition of cortical bone. Clin Orthop Relat Res. September 1978;135:192-217.

1983

Huiskes R, Chao EYS. A survey of finite element analysis in orthopedic biomechanics: the first decade. J Biomech. 1983;16(6):385-409.

Year	Entry
1994	Giori NJ. Mechanical Influences on the Differentiation and Modulation of Skeletal and Connective Tissues [PhD thesis]. Stanford University; July 1994.

Year

Entry

1994

Giori NJ. Mechanical Influences on the Differentiation and Modulation of Skeletal and Connective Tissues [PhD thesis]. Stanford University; July 1994.