Abstract
Human bones are susceptible to fatigue fracture under cyclic loading generated by repetitive activities which are a common health risk for the athlete and elderly populations. This work explores and summarizes the analytical and experimental methods used in current studies that investigate the fatigue fracture of human bones. Moreover, key parameters in those methods are identified that can be used for the development of standardized analytical and experimental methodologies for the investigation of fatigue fracture of human bones and ultimately lead to reliable prediction of their fatigue life.
Keywords: Human bone, Fatigue fracture, Crack initiation, Mechanics, Cyclic loads
1. Introduction
1.1. Bone fatigue fracture
Human bone fracture occurs either as a result of an impact event or due to fatigue caused by cycles of loads over time, often referred to as “fatigue fracture”. The cyclic loads leading to a fatigue fracture are often generated by typical repetitive activities and prolonged exercise. As such, fatigue fractures are a common health risk for the athlete and elderly populations. Fatigue fracture initiation is more prone to occur with exertion of atypical loads characterized by new, strenuous, and more severely repeated activities (9, Daffner and Pavlov, 1992) Bone damage, due to the application of cyclic loads, is defined as the initiation and enlargement of microcracks, which regularly occurs and is subsequently self-repaired (7, Chen et al., 2010) The phenomenon of bone self-repairing (bone remodeling), as a response to the incurred damage (bone resorption), is a biomechanical process through which the overall health of the human bone is preserved (Wolff's law). Based on the application of cyclic loads, the rate of bone resorption can be higher than the rate of bone remodeling (Tin et al.) This deficit can contribute to the propagation of microcracks leading to a bone fatigue fracture (12, Matcuk et al., 2016)
1.2. Mechanical fatigue fracture analysis
In mechanics (i.e. a branch of applied physics), fatigue fracture, caused by the application of cyclic loads, is described as a multi-phase phase process starting with a crack initiation phase and continuing into a crack-growth phase leading to a fracture. In the conventional method for the determination of crack initiation, each cycle of an applied load is considered to cause an infinitesimal amount of damage in the material. The damage in the material caused by a specific magnitude of load () is defined as the ratio of the number of load cycles () to the total number of load cycles that causes fracture () as (). For multiple magnitudes of loads, the cumulative damage is determined as the summation of the ratios corresponding to those induced stresses (). The fatigue fracture occurs when the cumulative damage reaches unity , (14, Miner 1945). For each externally applied load, an internal distribution of induced stress is developed. The conventional crack initiation method uses the results of experiments, on a specific detail with prescribed geometry and material, to obtain relationships between the induced stresses () and their corresponding numbers of cycles to failure (). The data constituting these relationships are statistically regressed and developed as S-N curves (Fig. 1). Using an S-N curve, for a given magnitude and number of induced stress for that detail, the remaining fatigue life can be determined using the developed S-N relationship (1, Basquin 1910).
Fig. 1.
A generalized S-N Curve.
1.3. Biomechanical bone fatigue fracture analysis - complexities
In biomechanics, prediction of fatigue fracture (fatigue life) for human bones is shown to be complex because of situational attributes including a) the existence of many bone details (bone geometric configuration and material), b) variation and randomness in the magnitudes and directions of cyclic forces generated by repetitive activities, c) patient's age, gender, size, bone density and state of health. Although previous studies have identified many factors that influence a patient's risk for fatigue fracture, a standardized analytical methodology for predicting fracture fatigue in human bones has not been developed. As such, development of conclusive S-N curves with consideration of all situational attributes has not been achieved.
1.4. Overview
In this work, the state-of-the-art analytical and experimental methodologies for determination of fatigue fracture in human bones are explored and summarized. In addition, key parameters in those methods are identified that can lead to the development of a standardized analytical and experimental methodologies for the investigation of fatigue fracture in human bones. As a part of this development, the results of the analytical methodology can ultimately be used for the development of a family of S-N curves that can reliably predict the fatigue life of human bones.
2. Methods
This paper focuses on sampling, testing and analytical methods from previous studies on bone fatigue fracture. The following provides a synopsis of relevant studies organized by bone type and characterized by their objectives and methods.
Carter and Hayes (4, 1976 and,5 1976) analyzed fatigue behavior of bovine femora cortical bone in bending at various temperatures and stress amplitudes. A total of 140 samples were formed into waisted cylinders with a length of 4.45 cm and a diameter of 0.457 cm. They were stored at −20 °C. During testing, wetness and a 37 °C temperature were maintained by submerging specimens in Ringer's solution. Samples were tested as a “fully reversed cantilever” at 125 cycles per second until fracture. The analysis focused on the relationship between the resulting S-N curve, the testing temperature and the bones' dry densities.
Bigley et al. (3, 2007) analyzed fatigue behavior of equine femora cortical bone in axial tension for samples of varying volumes. A total of 30 samples from 15 different racehorses were formed into waisted rectangular prisms with a varying length and a smallest dimension of 4 mm in the waisted region. They were stored at −20 °C. During testing, wetness and a 37 °C temperature were maintained by submerging specimens in a calcium-buffered saline solution. Samples were preconditioned for 100 cycles of sinusoidal loading at 2Hz, then subjected to 6 cycles of triangular loading at 2Hz to determine the elastic modulus, and finally subjected to sinusoidal loading with an amplitude set to produce 0.4% strain at 2Hz until fracture. 12 samples were not included in the analysis because they failed outside of the waisted region. The analysis focused on the relationship between fatigue life and bone volume. No S-N curves were developed in this study.
Lambers et al. (11, 2013) analyzed fatigue behavior of human vertebra cancellous bone in axial compression, focusing on microdamage and reductions in mechanical properties. A total of 32 samples from 16 donors were formed into cylinders with a length of 19 mm and a diameter of 8 mm. They were stored at −20 °C. Prior to testing specimens were glued into endcaps for attachment to the testing apparatus. During testing wetness and a 23 °C temperature were maintained by submerging specimens in a physiological buffered saline solution with 10 μM protease inhibitor. Samples were first evaluated for young's modulus with 10 cycles of 0–1% strain at 0.5% strain/second, then tested at room temperature in axial compression with sinusoidal loading at 4Hz until they had reached various levels of strain. The damaged volume fraction for each specimen was estimated visually from a cross section after testing. The analysis focused on the relationships between the damaged volume and various mechanical properties such as reduction in secant modulus, maximum strain, creep strain, energy dissipation, and number of cycles to failure (5% strain). No S-N curves were developed in this study.
O'Neal (15, 2011) analyzed fatigue behavior of human femora trabecular bone in axial compression for samples from donors of various ages. A total of 40 samples form 20 different donors were formed into cylinders with a length of 18 mm and a diameter of 5 mm. They were stored at an unspecified temperature. Prior to testing specimens were glued into endcaps for attachment to the testing apparatus. During testing, wetness was maintained by submerging specimens in a solution of 0.9% physiological saline and 10 μmol/L protease inhibitor. Samples were first subjected to a sustained load producing 0.8% maximum strain for 3 h to create an initial level of microdamage. Then they were preconditioned for 10 cycles of 0.05-0.045% strain and evaluated for young's modulus using the 10th cycle, then tested in axial compression with sinusoidal loading at 2Hz until the specimen reached 0.8% strain. Micro-CT scans were taken of samples at each stage in the testing process to evaluate microdamage. The analysis focused on the relationship between the levels of microdamage observed at various stages of testing and donor age. No S-N curves were developed in this study.
Mazurkiewicz and Topolinski (13, 2017) analyzed fatigue behavior of human femora trabecular bone in axial compression for samples of varying mineral content. A total of 57 samples from 57 donors were formed into cylinders with a length of 8.5 mm and a diameter of 10 mm. They were stored at room temperature in a 10% formalin solution. During testing wetness and a 37 °C temperature were maintained by submerging specimens in an 0.9% NaCl solution. Samples were tested in axial compression with stepwise loading of 500 cycles sinusoidal loading per step at a frequency of 1 Hz until failure. Failure was defined as the first cycle where the deformation increase was 10% greater than its mean value. Mineral content was also measured for each sample after testing. The analysis focused on the relationships of bone mineral density with fatigue life, cumulative elastic energy, and cumulative energy dissipation of the bone. No S-N curves were developed in this study.
Caler and Carter (6, 1989) analyzed fatigue behavior of human femora cortical bone in axial tension, compression, and reversed loading with varying loading frequencies. A total of 71 samples from 5 different donors were wet milled to form waisted cylinders with a length of 8 mm and a small diameter of 3 mm. They were stored at −20 °C. During testing wetness and a 37 °C temperature were maintained by wrapping specimens in water soaked tissue paper and dripping water over them. Samples were first evaluated for Young's modulus with 1 loading cycle of 14Ma, and then tested in axial tension compression, or reversed loading with sinusoidal loading at 2Hz or 0.02Hz until fracture. The analysis focused on the development of an S-N curve, as well as on the relationship between the normalized stress amplitude and the time to failure. A cumulative damage model resembling miner's rule was also developed for a single stress amplitude.
Pattin and Caler (16, 1996) analyzed fatigue behavior of human femora cortical bone in axial, tension, and reversed loading. A total of 32 samples from 9 different donors were wet milled to form waisted cylinders with a length of 8 mm and a small diameter of 3 mm. They were stored at −20 °C. During testing wetness and temperature were maintained by wrapping specimens in water soaked tissue paper and dripping water over them. Samples were first evaluated for Young's modulus with 1 loading cycle of 14Ma, and then tested in axial tension, compression or reversed tension and compression with sinusoidal loading at 2Hz until fracture. The analysis focused on secant modulus degradation as well as energy dissipation. Rather than modeling damage according to miner's rule, their equation for damage was based upon change in secant modulus.
Cotton et al. (8, 2005) analyzed fatigue behavior of human femora cortical bone in axial tension. A total of 40 samples from 4 different donors were formed into rectangular prisms with a length of 12 mm and a cross sectional area of 8 mm2. The storage temperature was unspecified. During testing, wetness and a 37 °C temperature were maintained by submerging specimens in Ringer's Solution, a saline solution designed to replicate bodily fluid. Samples were first evaluated for Young's modulus with 20 loading cycle of 12Ma at 2Hz, then tested in axial tension with sinusoidal loading at 2Hz until fracture. 11 samples were not included in the analysis because of premature failure or unreliable extensometer readings due to slippage. The analysis focused on the development of an S-N curve, as well as models for creep rate and damage rate. Rather than modeling damage according to miner's rule, their equation for damage was based upon change in secant modulus.
Turnbull (18, 2013) analyzed fatigue behavior of human femora cortical bone in axial tension and compression for samples from donors of various ages. A total of 48 samples from 4 different donors formed into cylinders with a length of 10 mm and a diameter of 3 mm. They were stored at an unspecified temperature. During testing, wetness and room temperature were maintained by submerging specimens in a phosphate buffered saline solution. Samples were first evaluated for Young's modulus with the first 20 of 240 preconditioning cycles of 40Mpa. They were then tested in axial tension and compression with sinusoidal loading with an amplitude of 45 MPa (tension) or 75 MPa (compression) at 2Hz until the specimen reached a 5% reduction in secant modulus, then overloaded to fracture in tension. Micro-CT scans were taken of samples at each stage in the testing process to evaluate microdamage. 14 samples were not included in the analysis because they could not be machined, failed prematurely, or failed outside of the gauge section. The analysis focused on the relationship between the levels of microdamage observed at various stages of testing and donor age. No S-N curves were developed in this study.
Baumann (2, 2015) analyzed fatigue behavior of human femora cortical in axial compression for samples of varying intracortical porosity and mineral density. A total of 80 samples from 10 donors were formed into cylinders with a length of 10 mm and a diameter of 3 mm. They were stored at −20 °C and wrapped in gauze which had been soaked in a phosphate buffered saline solution. Prior to testing, specimens were glued into endcaps for attachment to the testing apparatus. During testing, wetness and a 37 °C temperature were maintained by submerging specimens in a phosphate buffered saline solution. Samples were evaluated for Young's modulus with the first 20 of 240 preconditioning cycles of 40Mpa, then tested in axial compression with sinusoidal loading with an amplitude of 75 MPa at 2Hz until the specimen reached a 5% reduction in secant modulus. Then samples were overloaded to fracture. After each point in the testing procedure, samples were micro-CT imaged for evaluation of microdamage. Four samples were not included in analysis due to premature failure. The analysis focused on a finite element based approach of determining the relationships of porosity, mineralization, and microdamage with stress distribution during loading and fracture initiation. No S-N curves were developed in this study.
Taylor (17, 1998) compared results found in previous studies by considering volume effects. He concluded that sample size has a significant effect on bone behavior and noted that in order for mechanical testing to give an accurate depiction of bone behavior, the sample size must be large enough to include both laminar and cement lines within the sample.
Kruzic and Ritchie (10, 2008) summarized the progress of bone fatigue research. They noted that direct comparison between studies is not currently possible due to variations in test frequency, loading mode, and testing temperature.
3. Results
3.1. Sample configurations and preparation
3.1.1. Sample size (number of donors)
The sample size used varied from study to study. The majority of studies analyzed samples from 1 to 19 donors. Ranges for those studies are summarized in Table 1.
Table 1.
Sample size.
3.1.2. Sample geometric configurations
The geometric configurations (size and shape) of samples also varied from study to study. Because the material structure of bone depends on the bone source, only studies involving human bone are considered, and the variety of sample shapes and dimensions are categorized for human femora trabecular bone samples and human femora cortical bone samples.
3.1.2.1. Human femora trabecular bone samples
Two of the studies tested human femoral trabecular bone. Cylindrical shape samples were used in both studies, but with dissimilar dimensions. These values are summarized in the Table 2.
Table 2.
Human femora trabecular sample geometric configurations.
3.1.2.2. Human femora cortical bone samples
Five of the studies tested human femoral cortical bone. These five studies each used one of three distinct sample shapes, with consistent dimensions for each shape. The sample shapes and dimensions used are summarized in the Table 3.
Table 3.
Human femora cortical sample geometric configurations.
3.1.3. Solution for maintaining wetness
In an effort to simulate in vivo conditions during storage and testing, bones are typically hydrated during storage and testing. Because the bodily fluid of different mammals varies, only studies involving human bone are considered.
The liquid solution used to hydrate the bone varied from study to study. The majority of studies used a form of saline solution, although the exact makeup was different. The solution used in each study involving human bone is summarized in the Table 4.
Table 4.
Solutions for maintaining wetness of human bone samples.
| Solution | Reference No. |
|---|---|
| Saline Solution (physiological buffered with 10 μM protease inhibitor) | 11 |
| Saline Solution (0.9% physiological saline and 10 μmol/L protease inhibitor) | 15 |
| Storage: Formalin Solution (10%) Testing: Saline Solution (0.9%) |
13 |
| Water | 6,16 |
| Saline Solution (Ringer's) | 8 |
| Saline Solution (Phosphate Buffered) | 2,18 |
3.2. Testing procedure
3.2.1. Loading type
The loading was axial in all studies involving human femora bone. However, whether the axial loading was tension, compression, reversed loading, or a combination varied from study to study. Because the loading type expected in vivo depends on the bone source, only studies involving human bone will be considered and data are considered separately for human femora trabecular bone samples and human femora cortical bone samples.
3.2.1.1. Human femora trabecular bone samples
Two of the studies tested human femoral trabecular bone. Both of these studies loaded samples in axial compression.
3.2.1.2. Human femora cortical bone samples
Five of the studies tested human femoral cortical bone. The loading types used in each study are summarized in Table 5.
Table 5.
Human femora cortical loading types.
3.2.2. Loading frequency
The frequency of loading varied from study to study. Because the loading frequency expected in vivo depends on the bone source, only studies involving human bone will be considered and data are considered separately for human femora trabecular bone samples and human femora cortical bone samples.
3.2.2.1. Human femora trabecular bone samples
Two of the studies considered tested human femoral trabecular bone. The studies used different loading frequencies. One study used 2Hz loading frequency, while the other used 1Hz (13,15).
3.2.2.2. Human femora cortical bone samples
Five of the studies considered tested human femoral cortical bone. All of the studies analyzing human femoral cortical bone used a 2Hz loading frequency (2,6,8,16,18). One study also used a 0.02 Hz loading frequency for some samples, as the goal of the study was to compare fatigue life of samples subjected to different loading frequencies (6).
3.2.3. Load orientations
The loading shape varied from study to study. Because the loading orientations expected in vivo depends on the bone source, only studies involving human bone are considered which are separated for human femora trabecular bone samples and human femora cortical bone samples.
3.2.3.1. Human femora trabecular bone samples
Two of the studies considered tested human femoral trabecular bone. One study used constant amplitude sinusoidal load shape, while the other used stepwise sinusoidal loading (13,15).
3.2.3.2. Human femora cortical bone samples
Five of the studies considered tested human femoral cortical bone. All studies of human femoral cortical bone used a sinusoidal load shape (2,6,8,16,18).
3.2.4. Temperature
The temperature during testing varied from study to study. Because the body temperature varies for different mammals, only studies involving human bone will be considered. All studies involving human bone used a 37 °C testing temperature, with the exception of one study, which used room temperature (2,6,8,13,15,16,18). The reason for this deviation was cited as a desire to slow the rate of damage accumulation (18).
3.3. Analysis methods
3.3.1. Focus of analysis
The goal of analysis varied from study to study. Some studies focused on development of or variations in the S-N Curve, while others focused on relationships between fatigue life and levels of damage with various parameters. The focus of each study is summarized in Table 6.
Table 6.
Foci of analysis.
3.3.2. Definition of failure
The definition of specimen sample failure varied from study to study. Approximately, half of the studies considered fracture as failure. The remainder considered either a specific level of strain, increase in deformation, or change in secant modulus as indicative of sample failure. The method used in each study is summarized in Table 7.
Table 7.
Definitions of failure.
3.3.3. Definition of damage
The definition of specimen damage varied from study to study. Four studies quantified damage using a visual evaluation, two calculated damage from reduction in the secant modulus, one study generated a model for damage similar to Miner's Rule, and three studies omitted any discussion of damage accumulation altogether. The method used in each study is summarized in Table 8.
Table 8.
Definitions of damage.
4. Discussion
The results of this work confirm that, for bone fatigue fracture determination and life prediction, there exist key discrepancies in both analytical and experimental methods.
4.1. Analytical methods
For analysis methods, the key variations can be identified as the analysis focus, the definition of failure, and the definition of damage. Some studies focused on the development of an S-N curve, while others focused on different parameters’ effects on the total fatigue life or damage accumulation for a prescribed stress amplitude. The terms used to discuss bone damage also varied from study to study, with some studies omitting a discussion of damage altogether.
4.2. Experimental methods
For experimental methods, the key variations can be identified as sample preparation, testing procedure, and data analysis methods.
I. Sample Preparation: For sample preparation, the differences are in the number of donors, sample geometric configuration, and the liquid solution used to maintain wetness.
Number of donors: The number of donors used in a study influences the study's precision in representing its target population. In the studies examined, the number of donors varied from 4 to 57.
Sample Geometry: Sample geometric configuration (shape and dimensions) are influenced by the bone source, therefore only studies involving human bone were considered. Human femora trabecular bone samples were all cylindrical, but the proportions were dissimilar. Human femora cortical bone samples were varied shapes but had consistent dimensions for each shape.
Sample Solution: The solution used to hydrate bone samples was typically designed to simulate the bodily fluid of the bone source, therefore only studies involving human bone were considered. The majority of studies used a saline solution to hydrate bone samples during testing; however the exact make up of that solution was inconsistent and seldom specified in detail.
II. Testing Procedures: For testing procedures, the differences are in the sample loading and testing temperature.
Sample Loading: For sample loading, the differences are in loading type, loading frequency, and load shape. Axial (longitudinal) compressive loading was universally used for human femora trabecular bone. Axial loading was also used in all cases for human femora cortical bone, but the use of tension, compression, or reversed loading was inconsistent. Conversely, loading frequency was inconsistent between the two studies of trabecular bone, but 2Hz was always used for femoral cortical bone. A sinusoidal load distribution was used in all but one study. While the loading methods were somewhat consistent, studies generally lacked any stated logic for why different parameters were used.
Testing Temperature: Testing temperature was constant at 37 °C for all but one study. This temperature represents a typical body temperature and will be reasonable to include in a standard testing procedure.
III. Data Analysis Methods: For experimental data analysis methods, the differences are in determination of failure criteria (i.e. observation of crack initiation versus complete rupture) as well as the statistical approaches for data processing.
4.3. Recommendations
The authors recommend the development of a widely accepted analytical methodology, as a predictive model, that is: a) built on clear medically and biomechanically backed definitions for the notions of failure and bone damage b) based on the mechanical properties of human bone (with variations in geometric configuration and randomness in the loading patterns), c) built on the mechanics-based phenomena of fracture initiation (as an instantaneous brittle failure), and d) other situational attributes such as patient's age, gender, size, bone density and state of health.
Moreover, in order to ensure experiments obtain compatible data, the authors suggest the development of a standardized experimental methodology for evaluating human bone fatigue behavior, including recommendations for: a) sample preparation, b) testing procedures and, c) data analysis methods. Standard sample preparation guidelines will provide a recommended minimum number of donors, set sample dimensions, and specifications for a hydrating solution that closely resembles human bodily fluid. Standard testing procedures will provide a loading type, frequency, and distribution consistent with human activities, as well as a standard testing temperature based on human body temperature. Standard data analysis methods will define a medically and biomechanically backed definition for observing and determining sample failure and bone damage as well as a clear focus of data collection.
5. Conclusions
This work shows that for determination of bone fatigue fracture and fatigue life prediction, there exists no widely accepted analytical methodology based on biomechanical behavior. In addition, the state-of-the-art experimental methodologies have significant discrepancies in their procedures. In order to determine the fatigue fracture of the human bone, it is crucial to develop the predictive analytical methodologies capable of correctly modeling that phenomenon. Moreover, it is as essential to develop experimental methodologies in order to calibrate and validate the analytical models through standard data collection processes. With the eventual development of standardized analytical and experimental methodologies, it is envisioned that a fatigue life prediction tool (including a series of S-N curves for different bones and situational attributes) may be used by medical professionals to evaluate patients’ risk for bone fatigue fracture as well as the overall bone health of the patients.
Contributor Information
Demetria E. Boatwright, Email: dboatwri@hawk.iit.edu.
Mehdi Modares, Email: mmodares@iit.edu.
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