Biomechanical properties were assessed from the tibias of 17 adult males 17-46 years of age. Tissue-level mechanical properties varied with bone size. Narrower tibias were comprised of tissue that was more brittle and more prone to accumulating damage compared with tissue from wider tibias.
Introduction: A better understanding of the factors contributing to stress fractures is needed to identify new prevention strategies that will reduce fracture incidence. Having a narrow (i.e., more slender) tibia relative to body mass has been shown to be a major predictor of stress fracture risk and fragility in male military recruits and male athletes. The intriguing possibility that slender bones, like those shown in animal models, may be composed of more damageable material has not been considered in the human skeleton.
Materials and Methods: Polar moment of inertia, section modulus, and antero-posterior (AP) and medial-lateral (ML) widths were determined for tibial diaphyses from 17 male donors 17-46 years of age. A slenderness index was defined as the inverse ratio of the section modulus to tibia length and body weight. Eight prismatic cortical bone samples were generated from each tibia, and tissue-level mechanical properties including modulus, strength, total energy, postyield strain, and tissue damageability were measured by four-point bending from monotonic (n = 4/tibia) and damage accumulation (n = 4/tibia) test methods. Partial correlation coefficients were determined between each geometrical parameter and each tissue-level mechanical property while taking age into consideration.
Results: Significant correlations were observed between tibial morphology and the mechanical properties that characterized tissue brittleness and damageability. Positive correlations were observed between measures of bone size (AP width) and measures of tissue ductility (postyield strain, total energy), and negative correlations were observed between bone size (moment of inertia, section modulus) and tissue modulus.
Conclusions: The correlation analysis suggested that bone morphology could be used as a predictor of tissue fragility and stress fracture risk. The average mechanical properties of cortical tissue varied as a function of the overall size of the bone. Therefore, under extreme loading conditions (e.g., military training), variation in bone quality parameters related to damageability may be a contributing factor to the increased risk of stress fracture for individuals with more slender bones.
STRESS FRACTURES ARE overuse injuries of bone that are common among elite runners and military recruits.(1–3) Before injury, affected bones are typically normal with no acute injury. Morbidity from stress fractures ranges from minor pain to serious lifetime disability for the individual.(4) Stress fractures have been reported in the ribs, hip, spine, and metatarsals,(3, 5) but vigorous weight-bearing activities, such as running and jogging, commonly lead to stress fractures of the lower extremities, especially the tibia.(3) During basic training, 1–5% of U.S. male military recruits sustain a stress fracture.(2) However, this incidence is two to five times higher in female recruits.(6) Stress fractures lead to loss of manpower, valuable loss of training time, expense of medical care, and discharge of affected soldiers.(7) A better understanding of the factors contributing to stress fractures is needed to identify new prevention strategies that will reduce fracture incidence.
A number of risk factors for stress fracture have been identified including physical fitness, external hip rotation, body height and weight, age, race, gender, muscle mass, motivation, footwear, smoking, and family history of osteoporosis.(1, 4, 8–10) One of the best predictors of stress fracture risk is bone geometry. Specifically, having a narrow (i.e., more slender) tibia relative to body mass has been shown to be a major predictor of stress fracture risk and fragility in male military recruits(1, 2, 11) and male athletes.(12) A stress fracture is thought to be a consequence of transiently reduced tissue strength arising from increased resorptive activity (i.e., increased porosity) that acts to repair damage induced by vigorous physical activity.(13) Thus, stress fractures may be pronounced in individuals with more slender bones because smaller bone size is thought to lead to higher tissue-level stresses and thus increased damage accumulation.(1, 2) However, this postulate is based on the assumption that all bones are constructed in equivalent manners, and the contribution of variable tissue-level mechanical properties to stress fracture incidence has not been explored.
An examination of inbred mouse strains may help explain why bone size is a risk factor for stress fractures in the human skeleton. A comparison of adult A/J and C57BL/6J inbred mouse strains revealed that the bone slenderness was inversely related to mineral content (as measured by ash content) and, by correlation, tissue modulus and strength.(14) Mineral content has been shown to be positively correlated with tissue stiffness and strength.(15) These results suggested that bone morphology and mineral content were coordinately regulated so whole bone stiffness appropriately matched the mechanical demands imposed by weight bearing. However, the downside of regulating mineral content to match bone size was that mineral content was also negatively correlated with tissue ductility.(14, 15) We postulate that a similar reciprocal relationship between bone size and bone quality exists in the human skeleton. The intriguing possibility that slender bones, like those shown in animal models, may be composed of more damageable material has not yet been considered in the human skeleton.
The goal of this study was to determine whether tissue-level mechanical properties vary with bone size in the human skeleton. This was tested by assessing the biomechanical properties of tibias from young adult males. Understanding why bone morphology is a risk factor for stress fractures should lead to better identification of those at risk and, ultimately, to early diagnosis, treatment, and modification of training regimens.
MATERIALS AND METHODS
Tibias of 17 male donors (15 white, 1 Hispanic, 1 black) 32.9 ± 10.4 years of age (range, 17–46 years) were acquired from the Musculoskeletal Transplant Foundation (Edison, NJ, USA). Donor body weight and height were obtained from the source. Only donors with no known skeletal pathology were included in the study. The tibias were freshly harvested, wrapped in wet gauze, and stored in plastic bags at −40°C.
Whole bone morphology
Tibia length (L) was measured as the average distance between the distal articular center (the middle of the talar trochlear facet) and the two proximal articular centers (medial and lateral condyles)(16) using a large-capacity slide caliper with an accuracy of ±2.54 mm (Mantex Precision; Haglöf, Madison, MS, USA). Tibia width was measured in the antero-posterior (AP) and medial-lateral (ML) directions at 10% intervals from 30–70% of the total tibia length using a 300-mm vernier caliper with an accuracy of ±0.02 mm (Fowler Company, Newton, MA, USA).
Cross-sectional morphology was determined from 3-mm-thick middiaphyseal cross-sections cut at 30%, 50%, and 70% of the total tibia length (Fig. 1) using a diamond coated metallurgical saw (Model 660; South Bay Technology, San Clemente, CA, USA). A calibrated image of each cross-section was obtained using a digital camera at a 0.024 mm/pixel resolution. Image analysis software (IMAQ Vision Builder 6.0; National Instruments, Austin, TX, USA) was used to threshold each image and quantify cortical area (CtAr), the moments of inertia about the AP (IAP) and ML (IML) axes, the polar moment of inertia (J = IAP + IML), and the section modulus in the AP (J/APwidth/2) and ML (J/MLwidth/2) directions. Moment of inertia and section modulus were assessed because these geometric measures are related to the bending and torsional stiffness of intact tibias. A slenderness index (S) was calculated in the AP and ML directions as the ratio of the AP and ML section modulus values, respectively, to tibia length and body weight(17):
where L = tibia length (mm) and BW = body weight (kg). The section modulus has been shown to scale linearly with body mass.(17) The inverse ratio was used so that a tibia with a large slenderness value is one that is thinner or gracile for the weight and height of an individual. A small slenderness value reflects a stocky or robust tibia. All morphological traits were averaged over the three cross-sections for each tibia.
Bone sample generation
Cortical bone samples were prepared from the diaphysis of each tibia for biomechanical testing (Fig. 1). The three diaphyseal cylindrical sections were rough-cut into antero-lateral, antero-medial, and posterior regions. From each of these regions, one to three prismatic beams were cut using a diamond-coated metallurgical saw (Isomet; Buehler, Lake Bluff, IL, USA). The beams were machined to regular test samples using an automated CNC milling machine under constant irrigation (Modela MDX-20; Roland DGA, Irvine, CA, USA). Sample width (circumferential direction) was machined to 5 mm and length (longitudinal direction) was machined to 55 mm for all samples. Sample height (radial direction) was 2.5 mm except for four tibias with thin cortices, which were machined to 2.2 mm. A total of eight samples were generated from each tibia and randomly distributed to monotonic (n = 4) and damage accumulation (n = 4) test groups. All samples were stored at −40°C in gauze saturated with PBS with added calcium(18) and placed individually in airtight bags.
Monotonic failure properties
Tissue-level mechanical properties were assessed by loading four cortical bone samples from each tibia to failure in four-point bending at 0.05 mm/s (Fig. 2A) using a servohydraulic materials testing system (Instron model 8872; Instron, Canton, MA, USA). Specimens were submerged in a PBS solution with added calcium(18) and maintained at 37°C throughout all tests. Load and deflection were converted to stress and strain using the following equations, which take yielding into consideration(19):
where σ and ε are the stress and strain at the outer surface of the beam, M = applied moment, b = specimen width, h = specimen height, a = ½ the span between the upper two load points = 9 mm, L = ½ the span between the two lower load points = 21 mm, ϕ = angle of inclination = a/ρ, and d/dϕ is the derivative with respect to ϕ. The angle of inclination was written in terms of the measured deflection (Δ) by estimating the curvature (ρ) using standard beam equations. Mechanical properties were calculated from the stress-strain curves, and these included modulus, strength, total energy, and postyield strain (Fig. 2B). Modulus was calculated from a linear regression of the initial portion of the stress-strain curve. Yield was determined using the 0.2% offset method. Postyield strain was defined as the strain at failure minus the strain at yield. All properties were averaged over the four samples tested for each tibia.
Damage accumulation tests
Tissue damageability was assessed using a protocol designed to induce and accumulate cracks in cortical bone specimens. The accumulation of damage leads to measurable degradation of mechanical properties.(20) Therefore, the degradation of mechanical properties can be used as an index of matrix damage. Four cortical bone samples from each tibia were subjected to a fifteen cycle damage accumulation protocol (Fig. 3A) similar to that described previously.(21) For this protocol, “diagnostic” cycles (1, 3, 5, 7, 9, 11, 13, and 15) were interposed between “damage” cycles (2, 4, 6, 8, 10, 12, and 14). For the diagnostic cycles, the specimens were loaded in four-point bending at 0.5 mm/s to 50% of the average displacement at yield (determined from the monotonic tests), held for 60 s, and unloaded at 0.5 mm/s. Preliminary studies indicated that this load level provided information on tissue-level mechanical properties without inducing additional damage. For the damage cycles, the specimens were loaded at 0.5 mm/s to 50%, 75%, 100%, 125%, 150%, 175%, and 200% of displacement at yield, respectively, held for 60 s, and unloaded at 0.5 mm/s. A 5-minute recovery period followed each damage cycle. Displacement at yield was used as a reference in the damage cycles because this parameter showed little variation among the test samples when subjected to monotonic four-point bending. The displacement at yield was 1.0 mm for the samples with a height of 2.5 mm and 1.07 mm for the samples with a height of 2.2 mm.
A mechanical measure of the amount of damage that accumulated within the test sample was quantified from the magnitude of stiffness degradation. For each diagnostic cycle, stiffness was calculated from a linear regression of the initial portion of the load-deformation curve. Specimen stiffness decreased nonuniformly with each cycle revealing increasing amounts of damage induced within each cycle and an overall damage accumulation by the end of the protocol (Fig. 3B). At the end of the test sequence, the overall damage parameter, D, was calculated by comparing the stiffness of the first and last diagnostic tests such that:
where S15 is the stiffness of the last diagnostic cycle and S0 is the average stiffness of the first two diagnostic cycles (S1, S3) and the first damage cycle (S2).
All data were regressed against age using linear regression analysis to identify the properties that varied significantly with age (GraphPad Prism, San Diego, CA, USA). To determine whether bone morphology was related to tissue level material properties, partial correlation coefficients were determined between each geometrical parameter (e.g., IAP, IML, J, S) and each tissue level mechanical property (modulus, strength, total energy, postyield strain, damageability) while taking age into consideration (Minitab, State College, PA, USA).(22)
The sample population showed broad ranges of body size, body stature, and bone morphology values (Table 1). Modulus and strength showed little variation among individuals (CV = 9.73% and 4.62%, respectively). However, postyield strain (CV = 24.0%), total energy (CV = 26.4%), and the damage parameter (CV = 23.0%) all showed large variability among the samples. Morphological measures such as AP width, section modulus, and the polar moment of inertia, J (Fig. 4), increased linearly with body weight (R2 = 0.59, p < 0.003) and body mass index (BMI; R2 = 0.57, p < 0.004), but were independent of body height (R2 = 0.01, p < 0.7). These relationships did not change when the body weight values were corrected for age (data not shown). Body height was uncorrelated with body weight (R2 = 0.01, p < 0.8), indicating that the sample population consisted of individuals with similar heights but widely varying body weights.
Table Table 1.. Variation in Properties Among Young Adult Male Tibias
Significant age-related changes were observed for the tissue-level mechanical properties and the size of the tibia. A significant, positive correlation was observed between tibia slenderness in the AP (R2 = 0.31, p < 0.02) and ML (R2 = 0.24, p < 0.05) directions and age. However, IAP, IML, and J did not vary with age, suggesting that the variation in slenderness with age was due largely to higher body weight and BMI (R2 = 0.29–0.32, p < 0.03) values for the older individuals. Although tissue modulus did not vary significantly with age, tissue strength (R2 = 0.53, p < 0.001), postyield strain (R2 = 0.44, p < 0.004), and total energy (R2 = 0.32, p < 0.002) were significantly lower for the older individuals. Furthermore, a significant, negative correlation was observed between the damage parameter and age (R2 = 0.41, p < 0.006). This data suggested that, whereas the tibia became more slender relative to body size with age, the cortical tissue became progressively less strong and less ductile (i.e., more brittle) with age.
The correlation analysis showed significant correlations between tibial morphology and the mechanical properties that characterized tissue brittleness and damageability (Table 2). The relationships among tissue-level mechanical properties and cross-sectional morphology were linear. Post- yield strain and total energy increased significantly with AP width (Figs. 5A and 5B). Modulus decreased with IAP (p < 0.07), J (p < 0.08), AP section modulus (p < 0.05), and ML section modulus (Figs. 5C-5F). Tissue damageability increased with tibia slenderness in the AP (p < 0.05; Fig. 6) and ML (p < 0.09) directions. These correlations, which were independent of age, indicated that a narrower bone was comprised of tissue that failed in a more brittle manner and accumulated more damage.
Table Table 2.. Partial Correlation Coefficients Taking Age Into Consideration
The results of this study revealed that the tissue-level mechanical properties of cortical bone varied with the size of the tibia. Positive correlations were observed between measures of bone size (AP width) and measures of tissue ductility (postyield strain, total energy), and negative correlations were observed between bone size (moment of inertia, section modulus) and tissue modulus. Many of these correlations were significant. The lack of significant correlation with all measures of bone size can be attributed largely to the complex shape of the tibia. The tibia has a triangular cross-section and, consequently, measures of width correlated significantly with mechanically relevant traits like cortical area and moment of inertia but explained only 50–80% of the variability in these measures (data not shown). These correlations would be greater if the cross-section had a circular shape. The variability in these correlations was sufficiently large that neither the linear (width) traits nor the integrated traits like area and moment of inertia correlated significantly with a particular tissue-level mechanical property simultaneously. Nevertheless, the data indicated that bones with smaller width were comprised of stiffer and less ductile (i.e., more brittle) material compared with larger, more robust bones. The correlation between tissue ductility and bone size may help explain why male military recruits(1, 2, 11) and male athletes(12) with narrow bones show a higher incidence of stress fractures compared with individuals with wide bones.
The development of the slenderness index(17) was for a “normal” range in height and weight and is probably not useful beyond this range. However, the morphological variation observed in our sample population was consistent with that reported for military recruits(1, 2) and runners,(12) and height and weight were consistent with recent national averages.(23) As expected, bone size varied with body weight,(17) but did not vary with height (Fig. 4).(24) Thus, narrow bones came from less heavy individuals who were of similar height as those with wide tibias. Weight varied more than height for our sample population similar to that observed for the aged-matched national data. Furthermore, the variability in weight, specifically inclusion of one outlier (Fig. 4), did not affect the results (i.e., the heaviest person did not have an unusual slenderness value). Thus, the bones used in this study seem to be an appropriate size relative to body type.
The variation in long bone slenderness has been attributed to genetic and environmental factors influencing growth and development(25) and has been implicated as a risk factor for osteoporotic fracture.(26) To be relevant for military recruits, the sample population should have ranged in age between 18 and 25 years. However, for the age range in this study, the tissue-level mechanical properties varied linearly with age and were easily corrected using a linear regression method.(22) Consequently, the correlation analysis presented here provides relevant insight into the relationship observed between bone size and stress fracture risk for young adult males. Further studies are needed to determine if this relationship holds over a wider (older) age range.
The data provide a new paradigm that may explain how variation in bone slenderness contributes to stress fracture risk. Individuals with narrow tibias were previously thought to show increased fatigue damage during intense training because the smaller bone size would lead to an overload situation (i.e., higher tissue level stresses).(1, 2, 12) This interpretation was based on the assumption that tissue mechanical properties did not vary among individuals. However, the current results indicated that tissue-level mechanical properties do vary among individuals. Specifically, the data suggest that there are at least two important tissue-level mechanical property variations that need to be considered to understand why bone size is a risk factor for stress fractures. Narrower tibias were comprised of tissue that was more brittle (low total energy) and was prone to accumulate more damage compared with tissue from wider tibia. Having tissue that is more or less damageable may be inconsequential during day-to-day activities. However, tissue-level mechanical properties like total energy and ductility become particularly important in defining the response of bone to an extreme loading condition, such as that expected during military training or during a fall. Total energy defines the amount of energy required to break a bone (important during a fall) and ductility and damageability define the amount of damage accumulated under overload or repetitive loading (important during military training). Furthermore, tissue stresses would be expected to remain higher for narrow tibias loaded in bending or torsion. Moment of inertia is related to the external diameter raised to the fourth power. Because whole bone stiffness and strength are correlated with moment of inertia,(17, 27) a bone with a large external diameter should also show large overall stiffness and strength values. However, the ∼30% variation in tissue modulus (Table 1) did not fully compensate for the ∼100% variation in the moment of inertia or the section modulus (Table 1).(27) Thus, in situ damage accumulation may elicit a biological response (remodeling) that, coupled with the higher tissue stresses, exacerbates the fatigue process.(13, 28) Consequently, individuals with narrow tibia may be at higher risk of stress fractures because of higher in vivo tissue stresses (overloading) coupled with tissue that is more prone to accumulating damage.
The data may also help explain why age is another risk factor for stress fractures.(7, 29) Bone strength, postyield strain, and total energy decreased over the 17- to 46-year-old age range. This was consistent with previous studies(30–32) and indicated that cortical bone becomes less ductile (i.e., more brittle) and weaker with age and that these changes began early in life. This age-related decline in strength and ductility is thought to be a result of increased mineralization and remodeling.(33, 34) Thus, even in the young adult age range, the amount of damage accumulated under vigorous loading regimens would be expected to increase with age. This variation in tissue ductility may increase the susceptibility of stress fracture risk for recruits that enter into military training at an older age.
These results, and those of others, indicated that not all cortical tissue was constructed in the same manner. The mechanical properties of cortical tissue vary with age,(30–32, 35) across species,(35) among bones of the same individual,(36) and among anatomical sites within the same bone.(37, 38) Here we showed that the average mechanical properties of cortical tissue also varied as a function of the overall size of the bone. This coupling between bone morphology and tissue-level mechanical properties has been attributed to an adaptive response of bone.(14, 35, 39) In this study, smaller tibia bone size was coupled with an increase in tissue modulus. The goal of this adaptive response is to ensure that morphology and quality together meet mechanical demands. This coupling was observed when comparing bones subjected to widely varying mechanical demands from different species(35) and has also been used to explain the maturation of bone during growth.(40–43) Our current results suggested that this coupling might also exist for a particular bone (tibia) within the same species (human). Additional studies are needed to determine if similar relationships between morphology and quality exist for other long bones (femur, humerus, radius).
The relationship between morphology and tissue-level mechanical properties observed in the human skeleton was consistent with that observed for the mouse skeleton.(14) In both the mouse and human skeletons, genetic heterogeneity leads to variability in adult bone morphology and tissue level mechanical properties. A comparison of femurs from A/J and C57/BL6 (B6) inbred strains showed that A/J femurs were more slender than B6 as a result of the two strains having similar bone lengths, but A/J having a significantly smaller cross-sectional size and shape.(14) Despite the difference in bone size, the two strains showed similar whole bone stiffness values. The variability in bone slenderness was inversely related to mineral content, suggesting that bone morphology and mineral content were coordinately regulated so whole bone stiffness appropriately matched the mechanical demands imposed by weight bearing. However, as a result of regulating mineral content to match bone size, A/J femurs failed in a brittle manner and showed poor fatigue properties. In the human skeleton, smaller bones were stiffer and less ductile. Thus, a reciprocal relationship was observed between bone stiffness and ductility for both skeleton systems. This reciprocal relationship has been extensively reported for cortical bone,(15) and it is thought to be a result of the nature of the compositional and structural factors that can be modulated on a biological level.(44–47)Although variation in mineral content may have explained the differences in brittleness for the mouse skeleton, we expect that the human skeleton will be more complex and that the variation in tissue-level mechanical properties will be a consequence of variable composition (mineral, collagen, water) as well as microarchitecture (lamellae, osteon size, porosity).
The calculated bending modulus and strength values, which were determined from machined bone samples and were thus quantified in a manner that was independent of bone size, were consistent with bone tensile properties,(30) as expected. Test samples were randomly selected to obtain representative mean values for each tibia and the variation in mechanical properties within each tibia was similar to the variability observed across tibias. Thus, we believe that the mean values reported here represent the generalized tissue-level mechanical behavior for each tibia.
Compared with back-calculating tissue-level mechanical properties from whole bone failure tests, the current method of measuring tissue-level mechanical properties directly from machined samples provided a broader range of mechanical properties that were needed to better understand why bone size is a risk factor for stress fractures. The mechanical properties included measures of ductility (i.e., postyield strain, total energy) as well as an independent measure of damageability (i.e., the damage parameter). These properties were chosen because they were relevant for understanding the material response of bones subjected to the vigorous, repetitive loading associated with military training and running. Postyield strain and total energy represent measures of tissue ductility and were assessed to discriminate between ductile and brittle failure modes. Materials that fail in a brittle manner show low postyield strain and total energy values. Variation in the ductility of cortical bone arises from differences in the initiation, accumulation, propagation, and coalescence of damage in the form of microcracks.(48, 49) Variation in the damage parameter reflected differences in the amount of damage accumulated within the tissue and/or differences in the way damage degraded tissue stiffness. The damage parameter correlated negatively with postyield strain and total energy (R2 = 0.22–0.25, p < 0.05) indicating that cortical tissue that failed in a brittle manner also tended to have higher tissue damageability or, accumulate more damage. Although the ex vivo bending tests do not necessarily reflect the in vivo loads imposed on the tibia,(17, 50–52) the bending loads were expected to induce a combination of tensile, compressive, and shear damage(53) that may be sufficiently complex to represent a generalized variation in bone quality among human tibias.
The results of this study provide new insight into why bone size is a risk factor for stress fractures. Stress fractures are believed to be a consequence of excess damage accumulation following intense, repetitive activities. Biological processes that attempt to repair the damage may further weaken the tissue because the increased resorption results in increased tissue porosity.(54) However, the actual contribution of biological repair processes to stress fracture risk remains unclear.(55) Damage, in the form of microcracks, is the expected sequelae of repetitive loading following normal, daily activities.(56) Intense loading conditions, such as those associated with military training and long distance running, are expected to further increase in situ damage accumulation and degrade tissue-level mechanical properties.(13) Therefore, under extreme loading conditions (e.g., military training), variation in bone quality, specifically tissue damageability, may be a contributing factor to the increased risk of stress fracture for individuals with more slender bones. The current data suggested that bone morphology could be used as a predictor of tissue fragility and stress fracture risk in the absence of available noninvasive imaging techniques that accurately measure bone damageability.
The authors thank the U.S. Department of Defense (DAMD17–01-1–0806; DAMD17–98-1–8515) and the Musculoskeletal Transplant Foundation for their support of this research.