23 Numerical Simulation of Implants and Prosthetic Devices

10.1055/b-0035-122023

23 Numerical Simulation of Implants and Prosthetic Devices

Sebastian Eberle

Implants for fracture fixation and prosthetic devices for joint replacement have very different objectives. Implants for fracture fixation are meant to reduce and to stabilize the fracture fragments of a broken bone, so healing can take place. The final goal of a so-called osteosynthesis is to completely restore the bone′s preinjury tissue quality and functionality. Implants for fracture fixation have fulfilled their function after the healing process and are in fact often removed. By contrast, internal prosthetic devices are meant to grow into the bone as the bone grows around the prosthesis and completely replace a joint. The final goal of a total joint replacement is to artificially restore the functionality of an injured or arthritic joint.

However, both types of devices have to endure large loads within the human musculoskeletal system while sustaining their biomechanical functionality. The different aspects of this biomechanical functionality are often subject to biomechanical research studies to identify superior implants and treatment strategies. Most of the time, mechanical in vitro testing is employed to test the functionality of implants for fracture fixation and prosthetic devices (see Chapter 7 and Chapter 11 for details on mechanical testing in structural biomechanics). Yet, not all research questions and hypotheses can be addressed by biomechanical experiments. It is, for example, not possible to determine the strain or stress distribution within an intramedullary nail that is implanted in a bone. Furthermore, some in vivo processes cannot be captured by in vitro experiments (e.g., the biomechanical behavior of an ingrown joint replacement or in vivo loading scenarios with a large number of muscle forces). Finally, biomechanical research on implants by clinical studies is considerably restricted due to ethical reasons.

Numerical simulation methods like the finite element (FE) method have the potential to close these gaps in biomechanical research on implants. The FE method is a numerical method to compute approximate solutions of partial differential equations and integral equations (see Chapter 20 for details on the FE method). If the FE method is applied to solid continuum mechanics, displacements, strains, and stresses of solid structures subjected to load can be computed, which makes it very suitable for structural biomechanics. The application of the FE method is generally termed finite element analysis (FEA). Due to the capabilities of the FE method, the numerical simulation of implants and prosthetic devices by FEA has several advantages over experimental methods:

Virtual experiments are perfectly repeatable and reproducible. The effect of single parameters on the computed results can be analyzed. Each parameter variation can be computed with exactly the same initial conditions. This is usually not possible in biomechanical experiments.
Simulation models are completely observable. There is no need for measurement devices at specific locations that could influence the system.
Simulation models can be more realistic than biomechanical experiments, because they allow the application of physiological boundary conditions in terms of muscle forces and realistic joint kinematics.
Simulation models allow an “endless” number of parameter variations. Large sensitivity studies can be accomplished much faster and cheaper than with traditional experiments.

But, an FEA computes only an approximate solution and incorporates numerical errors and modeling errors due to simplifications and assumptions regarding the system behavior. These errors need to be verified and minimized to obtain reliable results. This can be accomplished by verification and validation within the process of modeling and simulation (Fig. 23.1). The goal of the modeling and simulation process is to transfer a conceptual model, which is a simplified representation of reality, into a computable simulation model. 1 By the process of verification and validation, it is assessed if the computational model is built right, and if it accurately represents the underlying physics of the problem.1

**Fig. 23.1** Schematic overview of the verification and validation process. (Figure taken from Anderson AE, Ellis BJ, Weiss JA. Verification, validation and sensitivity studies in computational biomechanics. Comput Methods Biomech Biomed Engin 2007;10[3]:171–184, with permission.)

Key Concepts: Verification

Verification is the process of determining that a model implementation accurately represents the developer′s conceptual description of the model and the solution to the model.” 2 Therefore, verification means to check the single procedures that are necessary to perform a simulation study for errors. Errors could be, for example, transposed digits, erroneous applied boundary conditions, or typos in a custom written code. A very important aspect of model verification in FEA is to check the numerical error of a FE model by mesh convergence analysis. Maxim: “Building the model right.”

Due to the process of verification and validation, it is obvious that a single simulation model cannot reliably address an arbitrary number of problems. Simulation studies are meant to solve a particular problem or to address a specific research question or hypothesis. Simulation should not be employed to an end in itself. In the end, the application of numerical methods in biomechanical research is similar to the employment of any other scientific method. Therefore, numerical simulation studies have to be planned as any other biomechanical research study.

Key Concepts: Validation

Validation is “The process of determining the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model.”2 Therefore, validation means to check if the chosen modeling approach and the made assumptions are appropriate to represent the aspect of reality that is of interest. In biomechanics, validation is usually accomplished by performing experiments and comparing the experimentally determined measurements to the computed values. Maxim: “Building the right model.”

23.1 Planning a Simulation Study

When planning a simulation study, two key issues have to be addressed:

What am I looking for? Which parameter do I want to compute? What is my research question, or what is the hypothesis I want to test?
Is the chosen numerical method the right method to determine that parameter or to test that hypothesis? Maybe there are other methods (analytical, experimental) that might be better suited, easier to perform, or even faster.

Potential parameters of interest in a bone-implant construct that could be computed by FEA are as follows:

Interfragmentary movements in a fracture fixation construct
Micromotions between bone and internal prosthesis
Strain or stress distribution in an implant with respect to strength
Strain or stress distribution in a bone with respect to strength or stress-shielding
Strength and stiffness of bone-implant contacts

When a parameter of interest is identified, the whole simulation study and the process of modeling and simulation should be oriented toward this parameter.

23.2 Modeling and Simulation

The process of modeling and simulation usually starts with a system analysis of the aspect of reality that is of interest. The goal of that analysis is to formulate a conceptual model, which is a simplified representation of reality with respect to the parameter that has to be computed (Fig. 23.1). The formulation of the conceptual model is probably the most important aspect of a simulation study. The following key issues have to be addressed for the modeling of a conceptual model of a bone-implant construct:

Which components or details of the in vivo situation need to be considered when a bone-implant construct is investigated (e.g., do I need to consider muscles, cartilage, or soft tissue?)?
Which components or details can be omitted with respect to the computed results? Do I need the lower leg with all muscles, tendons, and ligaments when my goal is to compute the interfragmentary motions in a femoral neck fracture?
What are the relations between the different components of the system? Is the implant bonded to the bone, or does it slide over the bone with a specific coefficient of friction?
What are the boundary and loading conditions? What are the joint kinematics, and how and where are forces applied?
How can components, relations, and boundary and loading conditions be simplified? Do I need a bone model with inhomogeneous and anisotropic material properties when my goal is to compute the stress distribution in an intramedullary device?
Where has nonlinearity to be considered or might be avoided? There are three sources of nonlinearity in an FEA:
- ○ Geometrical nonlinearity due to large displacements
- ○ Material nonlinearity (e.g., plastic behavior)
- ○ Nonlinear numerical contacts (e.g., friction contacts)

When the conceptual model is finally formulated, it has to be implemented in a computational model to be computable (Fig. 23.1). The two-stage implementation of the conceptual model into a mathematical model and then into a computational model is usually accomplished within the preprocessor of FE software packages. The preprocessing generally involves the following steps when developing an FE model of a bone-implant construct:

Building of the geometry. This is usually performed within computer-aided design (CAD)-like software packages. Surgical procedures like drilling, filing, cutting, or milling can be simulated by Boolean operations.
Discretization of the geometry by a meshing algorithm. Appropriate types of elements (e.g., shells, solids) have to be chosen and the necessary degree of discretization has to be determined by mesh-convergence analysis (see the following section titled “Verification and Validation”). 3
Application of material properties by constitutive laws (see Chapter 20). 4 If the inhomogeneous elasticity distribution of bone tissue has to be modeled, material mapping algorithms are employed that convert the bone density from q-computed tomography scans into elastic properties.4 However, not every research question within the topic of bone-implant constructs has to be addressed with such sophisticated approaches.
Application of boundary and loading conditions. For validation purposes, the boundary and loading conditions have to be analogous to the validation experiment. For experimentation, more sophisticated boundary and loading conditions might be applied. Muscle forces, for example, can be derived from musculoskeletal multibody models (see Chapter 19).
Definition of numerical contacts. This is maybe the most crucial part of modeling in FEA of bone-implant constructs. Contacts between implants and bone tissue generally involve friction unless the bone has grown around the implant until bone and implant are bonded. Therefore, the interaction between implants and bone has to be modeled with friction contacts. However, friction contacts are nonlinear and computationally expensive. Thus, it often makes sense to simplify contacts by bonding implant and bone together. A good example for such an approach is the bonding of the threaded part of a screw to the bone tissue (Fig. 23.2).