chapter  11
52 Pages

Analysis for Internal Fixation of a Fractured Bone by Means of Bone–Fixator Plate

WithDhanjoo N. Ghista, Sridhar Idapalapati, Ramakrishna Kotlanka

CONTENTS 11.1 Introduction and Scope ......................................................................... 306 11.2 Analysis of Forces in the Plate Screws of an Internally

Fixed Bone under Axial Loading......................................................... 307 11.3 Structural Analysis of Plate-Reinforced Fractured Bone under

Bending (to Determine the Forces Applied by the Screws) ............ 310 11.3.1 Bending Analysis of the Bone-Plate Assembly for

Stresses in Bone and Plate, Using Composite Beam Theory of Perfect Bond between the Bone and the Plate .............................................................................. 310

11.3.2 Bending Analysis of Bone-Plate Assembly, in which the Plate Is Attached to the Fractured Bone by Means of Screws.................................................................. 312 11.3.2.1 Analysis for Four Screws (Two on Each Side

of Bone Callus at the Fracture Site): Determination of Forces in Screws and Stresses at the Top of Bone Surface .................................... 312

11.3.2.2 Analysis of Six Screws (Three on Each Side of Callus at the Fracture Site): Determination of Forces in the Screws and Stresses at the Top of Bone Surface ..................................... 314

11.4 Finite Element Analysis of Bone Fracture Fixation .......................... 315 11.4.1 Representation of Constitutive Properties of Callus

and Plate for the Finite Element Analysis ............................ 315 11.4.2 Two-Dimensional Analysis of Internally Fixed

Fractured Bone under Bending, Using Stiffness-Graded Plate in Comparison with Stainless Steel Plate, for Perfect Bonding of the Plate to the Bone........................ 316

11.4.3 Two-Dimensional Analysis of Fracture-Fixed Bone with Stiffness-Graded Plate for Different Screw Locations ........ 319

11.5 Mechanics of Osteosynthesis Using Hemihelical Plates .................. 329 11.5.1 Bending Experiments of Straight Plate and

Fractured Bone Fixation Assembly with Different Screw Orientations ................................................................... 330 11.5.1.1 Materials and Methods ........................................... 330 11.5.1.2 Results and Discussion ........................................... 332

11.5.2 Hemihelical Plate versus Straight Plate Bone Fracture Fixation: Experimental Observations .................... 334 11.5.2.1 Materials and Methods ........................................... 334 11.5.2.2 Results and Discussion ........................................... 336

11.5.3 Hemihelical Plate versus Straight Plate Bone Fracture Fixation-Finite Element Analysis ........................ 339 11.5.3.1 Modeling of the Fractured Bone Fixation

by a Helical Plate ..................................................... 340 11.5.3.2 Loading and Boundary Conditions

Imposed on Fracture-Fixed Bone .......................... 341 11.5.3.3 Results and Discussion ........................................... 341

11.6 Conclusion ............................................................................................... 353 References ........................................................................................................... 355

Axial compressive load is more prominent in fracture-fixed long bones and hence internal fracture fixation by interfragmentary compression at the fracture site needs to be achieved. However, due to the applied load eccentricity (with respect to the central axis of the bone-plate assembly), bending moment is also applied to the fracture-fixed bone. Bending moment will induce both tensile and compressive stresses across the fracture site, and open up the fracture, leading to the reduction in the stability of the fixation. From an engineering perspective, fracture-fixed bone-plate assembly is weakest in bending though it gets subjected to axial compressive loading. Hence, in this chapter, we will analyze the plate-fixed fractured bone under compression as well as in bending loading. In this chapter, firstly using the composite beam theory based on the

mechanics of material approach, an analytical model is developed to calculate the forces in the screws used in bone fracture fixation by the plate. Based on the forces in the screws and stresses in the plate and the bone, an optimal selection criterion of the fixation plate is proposed to ensure minimal deformation of the fractured bone as well as for necessary and sufficient stress shielding. Secondly, employing the finite element method, the use of stiffness-graded plate as a potential substitute to the homogeneous

stainless steel bone-plate is analyzed to determine the extent of increased stress shielding. Thirdly, we demonstrate a novel concept of osteosynthesis using hemihelical plates for fixation of oblique bone fractures. Parts of this chapter are based on our work [1,2] concerning the biomechanical analysis of bone-plate assemblies.