Tornetta Rockwood Adults 9781975137298 FINAL VERSION

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CHAPTER 1 • Biomechanics of Fractures and Fracture Fixation

A, B

C

Figure 1-42.  A: Example of a finite element analysis (FEA) showing a proximal femur with a subtrochan- teric fracture, fixed by a cephalomedullary nail. The bone and the implant are represented by a mesh of individual “finite elements.” B: Physical validation of the FEA model by surface strain measurement on a surrogate femur with the same fracture model, implant, and loading condition. C: After successful valida- tion, FEA can readily determine the magnitude and location of stress concentrations, and can be used to perform a parametric optimization to reduce stress concentrations. (From Simpson H, Augat P. Experimental Research Methods in Orthopedics and Trauma . Stuttgart: Thieme; 2015.)

• A higher stiffness is not indicative of a stronger or more durable fixation construct. A less stiff or more elastic con- struct can prevent stress risers and may be beneficial in stim- ulating natural bone healing. • To predict the effects of construct stiffness on fracture heal- ing, the amount and direction of interfragmentary motion should be measured at the fracture site, and not inferred from actuator motion. • The strength of a fixation construct should be evaluated under dynamic loading and can only be determined if load- ing is continued until implant or fixation failure occurs. • A clearly defined failure criterion is required to determine construct strength in terms of the peak load, load level, or number of cycles until failure occurs. • Stability is not an engineering quantity and should therefore not be used for quantitative comparisons. • Stress cannot be measured directly. It can be calculated from strain or deformation measurements and the elastic modulus of the material. NUMERICAL SIMULATION There are two interrelated types of computational “ in silico ” simulations pertinent to fracture fixation constructs: FEA of fixation constructs for calculation of stress, strain, and defor- mation 206 ; and simulation of the bone healing process, driven by the effects of the transient mechanical environment on tissue differentiation. 101

FEA is the method of choice to analyze and optimize the design of implants to ensure sufficient strength while minimiz- ing stress risers. As described at the beginning of the chapter, equations exist to calculate stress, strain, and deformation of a beam with regular cross-section in response to a simple load. However, the geometry and loading of implants are more com- plex, requiring FEA to determine the mechanical effect of load- ing on the implant. In FEA, a computer model of the implant is created. The complex geometry of this model is then divided into many small “finite elements” that have a simple, regular shape (Fig. 1-42A). This process is called meshing, since the small elements cover the entire geometry with a uniform ele- ment mesh. Next, material properties are assigned to each ele- ment. Finally, specimen constraints and loading parameters are defined, simulating how the construct is constrained in its virtual test setup, and how loading is applied. The FEA soft- ware calculates the deformation of each element in response to loading, until the deformation of the entire model has been determined. Finally, a convergence analysis is conducted to determine if the model has a sufficiently large number of finite elements to calculate consistent results. Before a FEA model is employed to address a clinical question, it must be validated in direct comparison to results obtained in bench-top testing that exactly replicates the fixation construct, constraints, and loading. For example, in a model of a subtrochanteric femur fracture stabilized with a cephalomed- ullary nail, a bench-top test can determine the overall construct stiffness, and strain gauges can be used to measure surface

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