Introduction
Understanding biomechanics is essential for an orthopaedic surgeon. Orthopaedic surgeons are architectural engineers of the human skeleton and their job in trauma is to repair the skeletal structure if it is fractured or diseased so that it can resume its function. Doing so requires knowledge of the forces that caused the fracture and understanding of the destabilizing forces with potential to prevent healing. Effective fracture fixation requires implants and devices that counteract these destabilizing forces and promote healing ( Figs. 5-1 through 5-3 ).
The skeletal system allows us to move by providing a framework to which the muscles attach and provide power for movement. This movement is dependent on the integrity of the skeletal system as well as the muscular motors that are attached to it. Our understanding of the mechanics of this system and the mechanics of the devices we use in repair are critical to the restoration of our patients’ function.
The materials we use to repair the skeletal system are relatively basic. Most fixation devices are made of stainless steel, titanium, and cobalt–chrome alloys. These materials can be processed into various forms depending on the specific intended use in orthopaedic surgery. The material properties of these metals are critical to the function of the devices that are developed. In addition to the metal alloys, various forms of polyethylene and ceramics are also needed, particularly in joint arthroplasty.
The geometric design of a device also influences its mechanics. To properly design an implant for use in orthopaedic surgery, there must be a working knowledge of the material properties as well as the final mechanical properties of the device as it is designed. The surgeon must understand how these material and geometric properties interact in order to successfully treat patients. Biomechanics is the understanding of this science.
Grasping the basics of bioengineering requires that the orthopaedist understand the simple strain-stress curve as demonstrated in the following section, “ Basics of Mechanics .” This defines a material and tells us how much deformation or strain there is for the amount of stress that is applied to the material. The orthopaedist must also understand the basics of a load deformation curve that applies to the final design of an implant/bone construct. For example, the mechanical characteristics of a plate depend not only on its material but also on its geometry, the number of holes, and the placement of those holes. Similarly, intramedullary (IM) rods that have different designs or different diameters will have different responses to load. Each device must be able to carry the load needed to support the skeletal system until the bone heals and resumes its function. If the device is used to replace a joint, it must carry the load for a lifetime without fracturing.
The design of any device that repairs the skeletal system must take into account these engineering principles and the standard loads and displacement that one would expect to occur during movement of the skeletal system. Knowledge of the deforming forces that caused the fracture and displacement are key to successful application of stabilizing hardware.
In addition to the mechanical considerations, fracture fixation requires biologic and surgical considerations. The devices designed must be implantable through surgical windows and techniques and must be biocompatible. The design of these devices must be carried out with the combined effort of an orthopaedic surgeon who understands the anatomy and the biology, and an engineer who understands engineering design principles as well as the loads that the device must withstand. This chapter presents basic engineering principles that will allow an orthopaedist to understand the biomechanics associated with bone fracture, characteristics of materials and structures, as well as the capabilities that are required of these materials and devices to repair the musculoskeletal system.
Basics of Mechanics
Movement and/or Displacement
Engineering mechanics is fundamentally the study of the effect of forces on a body or an object. In general terms, when a force or load is applied to a body or object, that body either moves (a quarterback throws a football), deforms (the bend in a pole vault), or both occur (a club hits a ball) ( Fig. 5-4 ). Biomechanics is the application of mechanics principles to the human body. Both modes of force response (motion and deformation) are relevant in biomechanics. Under low-load conditions, the deformation of bones is fairly minimal and the propulsion of the body by the muscles is often considered only in terms of motion (i.e., assumes that the bones do not bend or twist). Substantial stretching or compression occurs in soft tissues, such as ligaments or cartilage, so those tissues are usually analyzed in terms of deformation ( Table 5-1 ).
| In Vivo Strain Range (%) | |
|---|---|
| Patellar tendon | 5–15 |
| Tibia | 0.07–0.9 |
Bone fractures require consideration of both motion and deformation. In this chapter, we will introduce the engineering fundamentals necessary to understand how bones fracture. This includes understanding material responses, structural characteristics, and bone loading. We will also give an overview of common fractures and address the basic mechanisms that promote fracture healing. Finally, we will address the mechanics behind some critical factors that affect both fracture risk and proper healing.
Stress/Strain
The local response of a material to an applied load is usually discussed in terms of stress and strain. Stress (σ) is defined as the force (F) applied to an object, divided by the area (A) over which the force is applied:
σ = F A
Therefore, two bones of different size may be loaded with the same force, but the smaller bone experiences a higher stress, due to its smaller area. This makes the smaller bone more prone to failure than the larger bone, assuming that the material properties and shapes are similar ( Fig. 5-5 ).
Similarly, strain (ε) is defined as the change in length (Δ l ) of an object divided by the initial length (L) of that object:
ε = Δ l L
The definitions given above for both stress and strain are for normal compressive and tensile stress (normal implies that the direction is perpendicular to the surface). In addition, there are equivalent concepts for shear stress and strain. Shear stress follows the same form as above, with the relevant force and area as indicated in Figure 5-6 .
Shear strain is defined as the parallel deformation divided by the perpendicular distance, which can be calculated as the tangent of angle α in Figure 5-6 .
Both stress and strain are actually three-dimensional entities fully described in terms of vectors or tensors. The same principles apply to the simplified two-dimensional analysis in a plane (anterior-posterior [AP] or medial-lateral [ML], for example), as for the full three-dimensional analysis.
Stress-Strain and Other Diagrams
Materials are often quantified and represented through the use of stress-strain diagrams. Stress-strain diagrams or graphs are typically generated from data obtained by performing a uniaxial tension or compression test of a small, well-formed sample of the material, such as the dog-bone shape shown in Figure 5-7 . In a uniaxial test, the sample of the material is pulled (or pushed) along the long axis of the object (uniaxial). The stress and strain are then plotted, and the resulting curve provides significant insight into the behavior of the material.
Properties of Materials (Young’s or Elastic Modulus, Yield and Failure, Energy/Toughness)
An example of a typical stress-strain diagram for steel is shown in Figure 5-8 . Several material properties can be determined from this curve. The elastic modulus (A), or Young’s modulus, of the steel is the slope of the linear portion of the curve (see point A in Fig. 5-8 ). Young’s modulus represents a general stiffness of the material. Stiffer materials (brittle) have a higher Young’s modulus. The material’s yield stress occurs at the end of the linear region, which is typically the point where irreversible damage begins occurring (see point B in Fig. 5-8 ). The yield stress of a material indicates that the material is beginning to fail or break. The ultimate, or failure stress represents the stress at which the material ruptures or fractures. The end of the curve (at the point where the stress abruptly drops to zero) represents this material’s failure stress or strength, and it occurs when the specimen breaks (see point C in Fig. 5-8 ). Finally, the area under the curve (see the shaded area in Fig. 5-8 ) represents the amount of energy expended in breaking the specimen. This is also known as the material toughness .
There are often trade-offs between the properties just described. A material with higher Young’s modulus (stiffness) often has lower toughness (energy). Similarly, high modulus and high strength are not necessarily correlated. A material may be brittle (with high modulus), but breaks at a low failure strength and, hence, has a low toughness. In the context of placing a stiff metal at an interface with tissues, such as bone and ligament, there can also be concerns regarding having too much stiffness, thus, inhibiting the motion that stimulates mechanobiologic feedback. Also, an abrupt change between a low stiffness ligament and a higher stiffness bone requires specialized tissue material properties and architecture within the transition zone. It is this transition zone interface that often causes difficulties in healing of ligaments, with the low stiffness region experiencing large tissue deformations leading to fibrous healing.
Other Material Properties (Viscoelasticity, Anisotropy, Creep and Relaxation, Fatigue, S-N Curve)
Several other important material properties cannot be determined from simple stress-strain curves. Most biologic tissues display some form of viscoelasticity, which simply indicates that they respond differently to forces depending on how fast the load is applied. In other words, viscoelastic materials have different stress-strain curves when they are applied at a fast rate (e.g., cutting maneuvers in sports) rather than a slow rate (e.g., yoga stretching). The amount of viscoelasticity in a material is represented by how much its stress-strain curves change for different rates of loading. Viscoelastic properties are often reported in terms of a dynamic modulus or a creep time–constant. Experimentally, viscoelastic properties are determined either by cyclically loading the material at different rates, or by conducting relaxation tests, where a sample is held at a constant load and the long-term change in deformation, or creep, is recorded.
Soft tissues, such as cartilage and ligaments, demonstrate high viscoelasticity, as shown in Figure 5-9 . Bone also has a viscoelastic response, but not as pronounced.
Another important characteristic of a material is its fatigue performance. Most engineering components fail not from a single high-magnitude loading event exceeding the material failure strength, but from the accumulation of repeated loading cycles occurring at a lower magnitude load. These lower load cycles form microcracks that expand over time and eventually lead to full-component failure ( Fig. 5-10 ). Because the number of cycles a material can withstand depends on the intensity or stress level, the fatigue performance of a material is often quantified through an S-N curve, where S is stress and N is the number of cycles, as shown in Figure 5-11 . These graphs show the number of cycles a material can be expected to withstand at a given stress level. The fatigue or endurance limit is defined as the stress below which cyclic or fatigue failure will not occur. Engineers design implants and devices so that their expected loading is well below the fatigue limit, so that they can be confident that the device will not fail over time in use. The safety factor is determined by the expected maximum in situ stress divided by the maximum allowable stress.
The caveats are that exact knowledge of the expected loading is complicated for a device in the human body that is capable of a multitude of activities and loading. For example, an Olympic long jumper will place higher stress on his or her lower limb on landing, compared with a high school long jumper or competitor in high hurdles. To our benefit, bones and musculoskeletal tissues are well suited to their normal activities, and also are known to adapt to the level of loading they are experiencing. For example, Olympic long jumpers may experience adaptation in their tissues to be able to resist the higher loading they are experiencing. However, there may be periods when activity has increased markedly, yet the tissue has not yet had time to adapt. This vulnerable period can lead to stress fractures where the bone material has not had time (or physiologic ability) to heal microcracks or adapt to the higher loading being experienced. A well-known situation for stress fractures is new military recruits participating in intense activity during their basic training period.
Within a biologically active tissue such as bone, fatigue is more complicated, as microcracks and even full fractures heal over time. In fact, the ability to repair microcracks is considered a unique property of bone, and one that is mediated through osteoclasts. Medications or conditions that impair osteoclasts (such as catabolic substances) can diminish the ability of the bone to repair microcracks and lead to brittle failure over time. As noted, certain classes of injuries, including stress fractures, are still fundamentally fatigue fractures ( Fig. 5-12 ). Of course, most mechanical failures of implanted hardware, such as plates, nails, or joint replacements, are also failures in the fatigue mode ( Fig. 5-13 ).
The material properties discussed in this section have been presented as if the materials were isotropic, that is, the properties are the same regardless of their orientation to the load being applied. This is true for most metals and traditional engineering materials. However, many materials, including most native tissues, have anisotropic properties, such that they have higher stiffness and strength in certain directions and orientations relative to the load ( Fig. 5-14 ). Soft tissues, such as ligaments and cartilage, have higher stiffness enforced by collagen fibrils along their length (or in multiple discrete bundles). Cancellous bone has anisotropic effects because of the microstructural arrangement of the trabecular network, which is different at separate anatomic sites. Most anatomic tissues are organized to have stronger and stiffer properties in the major direction of load. It is a matter of research whether occasional peak or maximum loading events are more efficient in evoking an adaptation to add bone, as compared with sustained lower level loading.
Finite Element Analysis Primer
Fundamental theorems in mechanics allow us to analyze deformation and stress in a variety of relatively simply shaped structures. However, finding analytical solutions for stress analysis in more complex geometries becomes much more difficult. For unstructured geometries, such as human bones, analytical stress solutions are impossible without substantial simplifications. For this reason, finite element analysis (FEA) is frequently used for biomechanical stress analysis.
FEA is a technique in which a complex geometry is subdivided into smaller pieces (the “finite elements”) for which the mechanical response can be described. As a simple example, consider Figure 5-15 . The simple cylinder under tensile loading in Figure 5-15, A has a known deformation response, but for the more complex geometry in Figure 5-15, B , a simple equation is no longer applicable. However, the complex geometry can be subdivided into three elements that resemble the simple cylinder, shown in Figure 5-15, C . This creates a linear system (set) of equations, which can be solved to reveal the deformation of the complex structure.
In a more generalized sense, the elements used in biomechanics applications are typically shaped as tetrahedral or hexahedral elements (pyramid or brick, as shown in Fig. 5-16 ). Figure 5-17 shows examples of a human femur meshed with both types of elements. In both of these cases, the ensuing analysis allows the calculation of stress and strain distributions throughout the bones. Knowledge of locations of particularly high stress indicates areas to evaluate as being more vulnerable to failure. Many examples of FEA related to fracture mechanics can be found ( Figure 5-18 ). FEA has been used to predict fracture patterns, evaluate fracture fixation devices, and study fracture progression at a microstructural level. As these examples show, FEA provides an alternative, or complementary approach to physical testing. FEA can provide information that cannot be measured experimentally, or facilitate large numbers of testing perturbations that would not be feasible for physical testing because of time and financial constraints.
Despite its increasing prevalence, and obvious advantages, there are several pitfalls that should be considered when evaluating FEA applications in biomechanics. First of all, the output of such analysis is only as good as the input data. Inaccurate imaging data (from which the geometry is created), material (tissue) property data, or loading (amount, orientation, timing) will all lead to incorrect results. FEA models should therefore include validation in the form of comparisons to a well-defined physical experiment. Otherwise, interpretation should be limited. Sensitivity tests can also be performed to evaluate the importance of model parameters that must be estimated or have high variability, such as material (tissue) properties. Additionally, FEA results can be sensitive to element size used, so ideally, a convergence test is performed to establish that the model results do not change with further decreases in element size. Figure 5-19 shows the effect of mesh size on the stress in a plate, and the discontinuous stress distribution that can result from using elements that are too large.
Despite these potential pitfalls, FEA has contributed significantly to our understanding of fracture mechanics and biomechanics in general. It has become a standard tool in the design of implants and fixation devices. In research applications, FEA has been used to study the effect of trabecular microstructure on fracture risk, and even to simulate the fracture healing process. As orthopaedic research continues to delve deeper into multiscale and multidisciplinary questions, FEA will become an increasingly important tool.
Bone Properties and Fracture Risk
From a mechanical viewpoint, bone is a material with mechanical properties that can be measured in the laboratory. These properties include the amount of deformation that occurs in the bone when it is placed under load, the mechanism and rate at which damage accumulates in the bone, and the maximum loads that the bone material can tolerate before catastrophic failure or fracture occurs. Additionally, the organized structure of bone allows it to function in various locations and conditions in the body. Its structural properties include the amount of deformation that occurs during physiologic loading and the loads that cause failure either during a single load event or during cyclic loading. Both the material properties of bone as a tissue and the structural properties of bone as an organ determine the fracture resistance of bone and influence fracture healing. This section includes a discussion of bone’s mechanical and structural properties and describes important clinical applications of these properties.
Bone Mechanical Properties
Bone provides structural support and allows for mechanical functions of our body. Its unique material properties and shape provide stability and allow for motion through its muscle attachments. Bone is not merely a rigid, homogeneous material throughout the body; rather, its composition varies depending on its location in the body and its primary function. Table 5-2 demonstrates the variation in bone properties at different points in the body.
| Anatomic Site | Relative Density | Modulus (MPa) | Ultimate Stress (MPa) | Ultimate Strain (%) |
|---|---|---|---|---|
| Proximal tibia | 0.16 (0.056) | 445 (257) | 5.33 (2.93) | 2.02 (0.43) |
| Femur | 0.28 (0.089) | 389 (270) | 7.36 (4.00) | Not reported |
| Lumbar spine | 0.094 (0.022) | 291 (113) | 2.23 (0.95) | 1.45 (0.33) |
* The mechanical properties of bone vary with location in the body. The relative density of bone and ultimate stress is the highest in the femur.
Bone is a living tissue composed of cells, water, and extracellular matrix. Mineral components make up 60% to 70% of the composition by weight; organic components make up 20% to 25%; and the remainder is water. The mineral components of bone consist of calcium hydroxyapatite and osteocalcium phosphate. Organic components of bone matrix consist of collagen, proteoglycans, proteins, growth factors, and cytokines. These organic components generally provide resistance to tension, while mineral components provide resistance to compression and stiffness ( Fig. 5-20 ).
The strength of bone tissue is gained predominately by the bone mineral and trabecular characteristics of connectivity and thickness. In orthopaedic literature, there is a large emphasis on the bone mineral density and its role in the risk of fracture. However, type I collagen makes up 90% of the organic matrix, and also contributes significantly to the mechanical properties of bone. Its fibril-forming structure provides tensile strength. A clinical example of collagen’s importance to bone strength and risk for fracture can be seen in osteogenesis imperfecta, a condition that causes a decrease in the amount of normal type I collagen ( Fig. 5-21 ). The orthopaedic complications with this disease include bone fragility and increased fracture risk. Previous studies that induced collagen denaturation in cadaver femurs, without changing the bone mineral, resulted in decreased toughness and strength.
The structure of bone constituents also influences its material characteristics. At the microscopic level, bone is either lamellar or woven. Lamellar bone includes both cortical and cancellous bone, and woven bone includes immature or pathologic bone. Woven bone has a random orientation of collagen and mineral. It is often made during periods of rapid bone formation, such as in fracture healing. Because of the arrangement of the tissue constituents, woven bone is weaker and more flexible. Lamellar bone, such as cortical or cancellous bone, consists of a structure that is oriented along the lines of major stress providing strength, while disorganized woven bone is not oriented according to applied stress. Figure 5-22 shows the microscopic differences of woven and lamellar bone. As discussed later, weaker woven bone compensates by producing more material and placing it further from the center as demonstrated with typical callus formation. Remodeling into more streamlined lamellar bone provides economy of material, with lower weight, while increasing resistance to the loads applied during activities.
