Biomechanical Model for Stress Fracture–related Factors in Athletes and Soldiers

Abstract

Stress fractures (SF) are one of the most common and potentially serious overuse injuries.

Purpose 

This study aimed to develop a computational biomechanical model of strain in human tibial bone that will facilitate better understanding of the pathophysiology of SF.

Methods 

The MRI of a healthy, young male was used for full anatomical segmentation of the calf tissues, which considered hard–soft tissues biomechanical interactions. From the undeformed coronal MR images, the geometry of bones, muscles, connecting ligaments, and fat were reconstructed in three dimensions and meshed to a finite element model. A force that simulated walking was applied on the tibial plateaus. The model was then analyzed for strains in the tibia under various conditions: unloaded walking, walking with a load equivalent to 30% of bodyweight, and walking under conditions of muscular fatigue. In addition, the effect of tibia robustness on strain was analyzed.

Results 

The model showed that the tibia is mostly loaded by compression, with maximal strains detected in the distal anterior surface: 1241 and 384 microstrain, compressive and tensile, respectively. Load carriage resulted in ~30% increase in maximal effective strains. Muscle fatigue has a complex effect; fatigued calf muscles (soleus) reduced the maximal effective strains up to 9%, but fatigued thigh muscles increased those strains by up to 3%. It had also been shown that a slender tibia is substantially prone to higher maximal effective strains compared with an average (22% higher) or robust tibia (39% higher).

Conclusions 

Thigh muscle fatigue, load carriage, and a slender tibia were detected as factors that may contribute to the development of SF. The methodology presented here is a novel tool for investigating the pathophysiology of SF.

Stress fractures (SF) are one of the most common and potentially serious overuse injuries among athletes and soldiers who are engaged in frequent and repetitive activity, especially in marching and running (¹). Although in recent years the incidence of SF among military recruits dropped below 12% (^2,3), this injury is still associated with substantive loss of training days, with mean time to return to preinjury activity of 21 weeks (^3,4). In severe cases, an untreated SF may result in a complete or displaced fracture, requiring surgical intervention. Although SF were reported to occur in most parts of the skeleton, such as in the femur, metatarsals, calcaneus, etc., 20%–60% of the SF in the active population occur in the tibia (⁵).

When a bone is loaded repeatedly, resulting in repetitive or cyclic strain, the subsequent accumulation of microdamage is believed to be the threshold of a pathological continuum that is clinically manifested as stress reactions and SF. Ultimately, if the activity is not ceased and the bone is not able to self-repair, a complete bone fracture might ensue. Notable, with increasing strains or greater strain rates, the number of loading cycles a bone can withstand before a fatigue failure occurs is reduced (⁶).

SF are frequently associated with populations that carry heavy loads, such as soldiers and backpackers (⁷). Although the effect of load carriage on physiological strains (e.g., cardiorespiratory and metabolic responses) and biomechanical loads (e.g., ground reaction, joint moments) is well documented (⁸), its effect on mechanical strains in bone tissues is less conclusive. A recent computational study, estimated peak compressive and tensile strains being 39.1% and 34.5% greater, respectively, when walking with 30% body weight load carriage (⁹). Using in vivo strain gauges, Lanyon et al. (¹⁰) showed that maximal compressive and tensile strains in the tibia were increased by 30% when walking with a 27-kg load, compared with a nonloaded walk. Burr et al. (¹¹) reported other results during a 17-kg loaded walk. Although compressive strains were comparable with those recorded during the unloaded walk, tensile strains were reported to be reduced by 13%. Noteworthy, however, strain gauge measurements are conducted at specific, discrete points on the bone surface and are likely to miss other areas that might be exposed to greater strains and which could be important in describing the damage cascade to the bone and the SF etiology.

Among the factors that lack consensus regarding their role in SF etiology is the effect of muscular fatigue on bone strain and the likelihood to develop SF. An animal study suggested that thigh muscles fatigue result in increased tibial strains (¹²), but in an earlier human study this effect was not observed (¹³). Milgrom et al. (¹⁴) reported that tibial tensile strains increased by 41% after a fatiguing march and that the compressive strains were reduced by 24%. Burr and Milgrom (¹⁵) concluded that mild muscular fatigue can result in significant increase in bone strains; however, severe fatigue may reduce bone strain values.

The search for a simple trait in bone morphology that can predict SF has been pursued extensively by many groups and over a long time now (^16,17). The effect of tibial morphological variability within young healthy populations on bone functionality was presented by Jepsen et al. (¹⁸). In this study, intrinsic constraints limited the degree of compensation for low robustness, leading to functional inequivalence relative to robustness, with slender tibia being as much as two to three times less stiff relative to body size compared with a robust tibia. In a subsequent study, Jepsen et al. (¹⁹) showed that in men engaged in elite-forces training, 78% of the SF occurred in individuals with slender tibia, or in individuals with average tibial dimensions but with impaired cortical area adaptation.

Despite the abundance of cohort studies, their contribution to the understanding of SF mechanisms and etiology is far from being sufficient. To substantiate firm conclusions, the isolation of each underlying parameter contributing to the development of SF would require large population size studies with a large number of SF occurring during the follow-up period. Modeling of biomechanical strains in bone tissue can help in overcoming the limitations associated with in vivo studies, both scientifically and in cost-effectiveness terms. With this perspective, the aim of the present study was to develop a computational model of bone strains in the human tibia, which will facilitate better understanding of the pathophysiology underlying SF, with a specific focus on the contribution of load carriage, muscular activity/fatigue, and tibial morphology parameters. For this purpose, we have developed a novel computational biomechanical model that considers the three-dimensional (3D) structural interactions between hard and soft tissues at the lower limb in the context of SF etiology.

METHODS

General

In this study, we evaluated strains in the bones of the calf that are expected to develop during walking, using a novel MRI-based finite element model, which considers the hard–soft tissue interactions in the lower limb. The MR scanning procedures applied in the study were approved by the ethical review committee of Sheba Medical Center, Israel (approval number 8560-11-SMC). Subject participation was approved after signing an informed consent form.

Anatomical geometry reconstruction

An MR scan protocol was developed for this research. The leg of a healthy, fit volunteer (22 yr, 81 kg, 1.89 m) was scanned for a full anatomical segmentation of the calf tissues in a one-piece image, from knee to heel. To ensure that no pressure was applied on the calf, the lower left limb was supported above the knee and at the heel. T1-weighted, 3-mm-thick slices of the calf were acquired in the axial planes. This scanning protocol provided the undeformed shape of the soft tissues of the calf. The MRI data set, which yielded the best image quality and spatial resolution for segmentation and modeling processes, was used to reconstruct the detailed 3D anatomy of the calf using ScanIP (Simpleware, UK) (Fig. 1). The tibia and the fibula were separated to cortical bone, trabecular bone, and bone marrow. The interosseous membrane (IOM) and the inferior anterior and posterior ligaments that transfer the loads from the tibia to the fibula (as one compartment) were also added. Then muscles were added, as a bulk of uniform soft tissue, and were enveloped by subcutaneous fat tissue.

FIGURE 1: The process of computational modeling of the calf. A, Undeformed MRI scans. B, Reconstruction of the calf tissues including the ligaments connecting the tibia and fibula. C, Meshing of the complete model. The fixed surfaces are marked with triangles and the loaded surfaces are marked with arrows.

Finite element modeling

Using ScanIP, the model was meshed with linear tetrahedral elements. The elements had been optimized so the in/out quality ratio was higher than 0.2. The model was exported to the Preview module of the finite element software FEBio (version 1.19) for assigning material properties, boundary, and loading conditions, and then it was analyzed by the FEBio solver version 2.5.2. Results were visualized and analyzed using the PostView module version 1.10 of the same software (Both Preview, FEBio, and PostView were provided by the Musculoskeletal Research Laboratory, University of Utah, Utah, USA, http://mrl.sci.utah.edu/software/febio). The runtime of each model variant was approximately 3 min using a 64-bit Windows 7–based workstation with Intel Core i7-5820K, 3.30 GHz CPU, and 32 GB of RAM.

Material properties and constitutive laws

Material properties were adopted from the literature for each tissue type: cortical bone was assigned orthotropic elastic properties of E₁ = 6.91 GPa, E₂ = 8.51 GPa, and E₃ = 18.40 GPa, and Poisson’s ratio: ν₁₂ = 0.488, ν₂₃ = 0.142, and ν₃₁ = 0.315 (²⁰). Trabecular bone was assigned orthotropic elastic properties of E₁ = 202 MPa, E₂ = 232 MPa, and E₃ = 769 MPa, and Poisson’s ratio: ν₁₂ = 0.420, ν₂₃ = 0.230, and ν₃₁ = 0.417 (²¹). Bone marrow was considered as fat tissue (with properties as specified below). Ligaments were assumed to behave as homogeneous isotropic linear-elastic materials, whereas the other soft tissues—muscle, fat, and skin—were considered hyperelastic. On the basis of the data published by Minns (1976), the IOM was considered as an isotropic material with an estimated effective elastic modulus of 200 MPa and a Poisson’s ratio of 0.4 (²²). The ligaments connecting the tibia and fibula were assigned an elastic modulus of 143 MPa and a Poisson’s ratio of 0.4 (²³). The muscle and fat plus skin (as one effective material) were assumed to behave according to the compressible Neo-Hookean strain energy density (SED) function W with material properties as reported elsewhere (²⁴).

Boundary and loading conditions

A total force equivalent of 3.5 times body weight (2800 N) was applied on the tibial plateaus (Fig. 1). These knee forces represent the second peak of load obtained during the stance phase (push off), as previously reported for healthy humans during walking (²⁵). This force was distributed on two separate surfaces, the lateral and the medial tibial plateaus, which were loaded with 880 N and 1920 N, respectively (²⁵). The proximal end of the tibia was allowed to move along the z axis (vertical axis), whereas the distal end of the tibia was fixed at the tibia–talus interface surface to prevent rotational and translational movement. The contact angles were 3° for the shank angle (coronal plane) and 4° for the rear foot angle (sagittal plane). Because potential boundary effects could be expected according to the Saint Venant’s principle from the theory of solid mechanics, our volume of interest (VOI) was defined to be far enough from these boundaries (10% of the tibial length in the proximal end to 90% of the bone length in the distal end).

Validation of the reference model

To validate that the strain values obtained from the computational simulations are within the physiological expected range, the results were compared with in vivo strain gauge data published in the literature (Table 1) (^{10,11,14,26–31}). Only publications that represented the bone deformation in specific terms of tensile and compressive strains were used for this comparative analysis. In the aforementioned studies, the strain gauges were attached at the anteromedial aspect of the midshaft of the tibia, and thus, for validation, the same anatomical site was used to extract the in silico results of the present study.

Model variants

An initial feasibility tests that represent the model sensitivity to biological variability in tissue mechanical properties was performed as was reported elsewhere (⁵). In total, nine models were built and analyzed, one as a basal condition (“reference model”) and eight as variant models (Table 2). In these models, geometry, boundary conditions, and mechanical properties of the tissues were clamped as in the reference model. For each model variant, a simulation was run once. Because the model uses a numerical computational approach (i.e., deterministic and not stochastic), each run generates the same result.

Effect of load carriage

The loads that were detailed above for the reference model were modified to represent walking while carrying a load equal to 30% of body weight. On the basis of previous studies, this condition was simulated by increasing the tibial plateau load by 26% (⁸) and by increasing the force applied by the soleus by 50% (³²). Although other muscles’ activity may be altered during load carriage, only the soleus is substantially affected during the simulated time point of the stance phase (i.e., the second peak of ground reaction forces).

Effect of muscular fatigue

Muscle activity was included in the model by adding the muscle forces that are exerted on the tibia during the simulated peak load at the stance phase. This included the following muscle bundles: tibialis anterior, soleus, quadriceps femoris, and also the iliotibial band (representing the force transferred from the tensor fasciae latae and gluteus). Because it was not feasible to detect from the MRI the exact muscle attachment site, the location, direction, and magnitude of these forced were obtained from Duda et al. (³³). By applying these muscle forces, the basal contribution of the muscle force to bone strain was simulated. Then the effect of fatigued muscles was simulated by applying a 40% lower force compared with the “reference model.” This condition represents an extreme muscular fatigue of all the muscles groups included in the model (¹⁴). In addition, to quantify the effect of each muscle group on the bone strain during fatigue, four individual muscle fatigue models were created, whereas the others remained as in the reference model (Table 2).

Effect of bone morphology variability

Bone robustness was calculated as the ratio between the cross-sectional area of the tibia at 38% of its length (measured from the ankle) and the tibial length (¹⁸). For the “reference model,” this value was considered as 1.0, which represents an average robustness of the bone (¹⁹). To simulate the effect of bone morphology on bone strain, the tibial length was clamped (402 mm), and all the tissues from the reference model were scaled in the axial plane, enabling to create robust and slender calf models. From previous human cohort data (¹⁹), robustness values of 0.8, 1.0, and 1.2 represent a slender, an average, and a robust tibia, respectively. These models yielded bimalleolar widths of 62, 67, and 72 mm, respectively.

Data analysis

Tensile and compressive strains were used as the outcome measures for comparison both for the validation measurements compared with the in vivo data, as well as between the reference model and the model variants. Because of the large amount of nodes and data points, to allow a meaningful analysis for the anterior and posterior paths VOI, a data reduction process was implemented, so that for every ~1 mm, the maximal strain value was detected and analyzed. For a straightforward detection of potential trends of effects, the effective strain was also calculated and reported. This scalar value, based on the von Mises criterion, indicating the combined contribution of both the compressive and the tensile loads, facilitates a straightforward direct comparison of strain data across simulation conditions. The effective strain is defined as follows:

For each outcome measure, the overall effect of each condition at every z position along the VOI, with respect to the reference model, was calculated: the average effect, i.e., the average percent difference compared with the reference model throughout the VOI; the minimal effect, i.e., the minimal percent difference compared with the reference model throughout the VOI; and the maximal effect, i.e., the minimal percent difference compared with the reference model throughout the VOI. In addition, for each simulated condition, Pearson’s correlation coefficient was calculated between the effect magnitude and the strain magnitude, and between the average effect and the effect at the maximal strain position.

RESULTS

The calculated anteromedial midshaft strains (the “strain gauge site”) are presented in Table 1. The simulated strains (tensile and compressive) were lower in a fatigue condition and higher while carrying a load than under the reference condition.

For each simulated condition below, the maximal strain and effect are presented in Table 2. Generally, weak to moderate negative correlation was observed (0.0 to 0.7), i.e., the effect was generally higher for sites with lower strain. In addition, a very strong correlation was found between the magnitude of effect at the maximal strain site and the average effect for each VOI: correlation coefficients were 0.91 for the anterior VOI and 0.99 for the posterior VOI.

Strain distribution along the tibia

Along the anterior cortex of the tibia, the maximal tensile and compressive strains were 384 microstrain and 1241 microstrain, respectively (Fig. 2A), which were observed 77 mm from the distal end of the tibia (19% of the tibial length). Along the posterior cortex, the maximal tensile and compressive strains were 277 microstrain and 868 microstrain, respectively, and were located 163 mm (41%) from the distal end of the tibia (Fig. 2B). These sites of maximal strains remained unchanged for all the simulated model variants.

FIGURE 2: Tibial strain while carrying 30% body weight compared with nonloaded walk. Tensile strain (positive values) and compressive strain (negative values) distribution along a pathway of the anterior cortex (A, marked in dashed line) and the posterior cortex (B).

The effect of load carriage

Load carriage (30% of body weight) resulted in up to 32% increase in the maximal strains along the anterior tibial surface (Fig. 2A) and 29% increase in maximal strains along the posterior tibial surface in comparison with the reference model values (Fig. 2B). At the midshaft of the tibia, the compressive and tensile strains were increased by 60% and 37%, respectively, along the anterior aspect and by 31% and 33% along the posterior surface of the tibia.

The effect of muscular fatigue

At the anterior and posterior surfaces, where maximal strains were detected, muscular fatigue resulted with similar reduction in the tensile and compressive strains (7% and 11%, respectively) (Table 2). This effect was not uniform along the tibia, which for example at the mid-anterior tibia was only 4% in tensile strain and 1% in compressive strain (Fig. 3). However, each muscle bundle contributed differently to the maximal strains. An increase of 3% in the maximal effective strains was noted by a fatigued iliotibial band or quadriceps, whereas the fatigued tibialis anterior and soleus induced a decrease in the maximal effective strains of 6% and 9%, respectively (Table 2).

FIGURE 3: Tibial strain during muscular fatigue compared with nonfatigued walk. Tensile strain (positive values) and compressive strain (negative values) along a pathway of the anterior cortex (A, marked in dashed line) and the posterior cortex (B).

The effect of bone morphology

In comparison with a “regular” (reference) tibia geometry, for a slender tibia, an increase of 36% and 22% in the maximal compressive and tensile strains, respectively, was calculated at the anterior surface. At the posterior surface, an increase of 22% and 16% in compressive and tensile strains was developed, respectively (Fig. 4, Table 2). In a robust tibia, compared with a “regular” tibia, a decrease of 10% and 13% in maximal compressive and tensile strains, respectively, was calculated and a decrease of 23% and 20% in maximal compressive and tensile strains along the posterior surface, respectively, was noted (Fig. 4, Table 2).

FIGURE 4: The effect of tibial robustness on bone strain. Tensile strain (positive values) and compressive strain (negative values) distribution along a pathway of the anterior cortex (A, marked in dashed line) and the posterior cortex (B) for tibial robustness of 1.0 (average), 0.8 (slender), and 1.2 (robust). The influence on the effective strains observed at the 38% cross section is shown in panel C. A, anterior; P, posterior.

TABLE 1: Anteromedial midshaft strains in the tibia; current study (in silico) compared with previous studies (in vivo).

TABLE 2: Summary of maximal strains, midshaft strains, and overall effect compared with the reference model.

DISCUSSION

The computational model developed in the current study, in which the hard–soft tissue interactions in the lower limb in the context of SF risk are considered, enabled to successfully predict the strains in the tibia under various simulated loading conditions that are relevant for walking and marching, with and without backload.

For the “reference model” (natural conditions of walking with nonfatigued muscular activity and a bone morphology robustness score of 1.0), the maximal anteromedial midshaft strains were within the physiological range that was reported in previous studies (^{10,11,14,26–31}); tensile strain = 160–840 microstrain and compressive strain = 308–1195 microstrain. This ensured a validated analysis by the model within these ranges of loads and strains.

The current study further facilitates deeper understanding regarding the nature and distributions of strains along the tibia. Previous in vivo strain gauge–based human studies that were conducted to investigate this aspect are controversial. Typically, those studies provide measurements at a particular point along the tibia, which is sensitive and prone to errors. Such an approach cannot disclose the paths of load transfer in the bone. Accordingly, our study is in accord with the claim of Yang et al. (³⁴), in which the use of a discrete strain gauge to characterize strains along the entire tibial length may be inadequate. In fact, peak compressive and tensile strains in the distal anterior cortex of tibia were substantially greater than those induced in the midshaft cortical bone, which cannot be described by the common single measurement site technique used in vivo by means of a strain gauge. Obviously, a full in vivo strain distribution analysis is currently not feasible using the current strain measurement techniques because of their invasiveness.

Some studies reported greater compressive strains compared with tensile strains at the anteromedial midshaft of the tibia (the “strain gauge site”) during walking, while other studies reported an opposite trend in strain behavior under similar or equivalent loading conditions (^26–28). Our results support the mechanism, in which at peak ground reaction forces during walking, the tibia is mostly loaded mainly by compression, and the resultant bending and tensile strains are generally lower.

Heavy load carriage, which concomitantly increase ground reaction forces and increase muscular activity, resulted in a substantial increase in bone strains. This, combined with the greater increase in the anterior VOI strains compared with the posterior VOI strains, suggests a complex and nonlinear response to the change in loading conditions. These results are in line with a recent computational study that investigated the effect of load carriage on an isolated tibia (⁹). The ~30% increase in tensile and compressive strains at the anteromedial midshaft is in agreement with the in vivo results published by Lanyon et al. (¹⁰) but contradict the results of Burr et al. (¹¹), who reported a reduction in tensile strains, and comparable compressive strains, during load carriage (Table 1). The substantial increase in tibial strains during load carriage, for which the effective strain exceeded 2000 microstrain, can substantially decrease the fatigue life of bone tissues (i.e., the number of repetitions required to cause a failure) and result in the earlier onset of SF (³⁵).

In vivo studies that directly examined the effect of muscular fatigue on tibial bone strains were not conclusive (^13–15). This might be due to confounding factors, such as age and systemic fatigue, that may alter gait and posture control. The present computational modeling enabled to analyze the complex effect of the muscles on tibial strains. We showed that when the muscles that are attached to the tibia are in fatigue state, tibial bone strains are slightly reduced. A more meticulous analysis that studied the contribution of each muscle group revealed that fatigued thigh muscles slightly increase bone strains, whereas fatigued calf muscles reduce bone strains. In male military recruits and in female athletes with lower limb SF, muscle strength (in a nonfatigue state) was found to be reduced, suggesting that muscles strength may have a protective effect against the development of SF (^17,36). These epidemiological studies, corroborated by our current simulation with the fatigued muscles, suggest a composite effect of the muscle forces. On the one hand, adequately synchronized muscle force activation pattern is essential for attenuating bone strains (thigh muscles), but on the other hand, calf muscle forces contribute substantially to the axial loading and the resultant strains in the tibia and, thus, are essential for maintaining proper bone strength (³⁵).

The present simulations showed that a slender tibia is exposed to maximal tensile strains, which are up to 50% greater compared with a robust tibia with identical mechanical properties. Inferior bone geometry parameters, such as a smaller cortical area (³⁷), a smaller area moment of inertia (^38,39), and a smaller bone width (^16,36,37), were previously associated with the increased risk to develop SF. Recently, in a cohort of healthy young subjects, it has been shown that a slender tibia is two to three times less stiff relative to body size, compared with a robust tibia (¹⁸). In a subsequent study, Jepsen et al. (¹⁹) showed that 78% of the SF in soldiers engaged in elite forces training could have been attributed to a slender bone (low robustness), or to an average robustness bone but with impaired functional adaptation. The current study allows to quantify bone strains for a range of physiological tibial robustness values under loading conditions that simulate walking (compared with bending tests that were performed in vitro). Importantly, the quantification and analyses of tibial strains considers the restraining effects that the bone-enveloping soft tissues (the IOM, ligaments, muscle, and fat) have on bone bending while bones are weight bearing, which has never been considered in previous published studies. The small differences between our results compared with the data of Jepsen et al. may be attributed to the fact that on top of the aforementioned bending effect, the tibia is loaded during walking by dominant axial compression; thus, the bending resistance may be overweighed in the aspect of SF etiology.

Low or high bone robustness is typically compensated for by increasing or reducing tissue mineral density or cortical area. However, complete compensations cannot always be achieved, as biological constraints limit the amount of compensation permissible (¹⁸). By clamping the bone properties between the models, our results represent the extreme cases that were observed in human cohorts, where no compensation occurs for slender or robust tibia, i.e., highest risk and lowest risk, respectively, resulting in insufficient or optimal functionality. Thus, the modeling methodology used in the current study may be helpful in identifying individuals at risk to develop SF, based on their lower limb morphology, as well as for other applications of musculoskeletal modeling.

Until a more developed technological tool can be available in the field, the current results suggest that by measuring the bimalleolar width of the ankle a simple anthropometric score can be deduced, indicating the tibia slenderness. This may serve as a simple surrogate for robustness and the risk of tibial SF (¹⁷). This, however, warrants further investigation in field studies.

The results of this study should be interpreted with caution and regarded as trends of effects rather than as absolute values. The modeling framework is based on a specific leg anatomy of a young healthy individual, with a specific bone curvature. Although the width of the bone has been virtually manipulated for investigating the effects of robustness, other geometrical features of the bone may vary across individuals but were kept as constants in the present work. These other bone morphology parameters such as radii of curvatures at the shaft or diaphysis parts could result, for example, in different bending intensities for different individuals. To make the present calculations and analyses computationally feasible and to reduce the number of the assumed values for parameters in this large-scale and anatomically detailed 3D modeling work, the model uses a quasistatic analysis. The model design was considering the axial knee forces at a single time point in the gait cycle, whereas in reality the reaction is fully dynamic, with some inertial, rotational, and viscoelastic effects at the bone tissue level. Thus, aspects like viscoelastic effects, shear strain, and strain rates were not included in the present analyses but warrant future investigations. Nevertheless, the present study results were validated compared with in vivo data to provide a confidence that the model predictions reflect the physiologically expected values.

CONCLUSIONS

A new anatomically comprehensive and accurate model of the calf was developed for successfully determining the tibial bone strains that develop during walking under different conditions, which might affect the onset and development of SF. The model showed that the tibia is mostly loaded by compression, with maximal strains detected in the distal anterior surface. Load carriage substantially increases tibial strains. Muscle fatigue has a complex effect: fatigued calf muscles reduce bone strains, but fatigued thigh muscles slightly increase bone strains. It has also been shown that a slender tibia is substantially more prone to high bone strains compared with average or robust tibias. Overall, thigh muscles fatigue, load carriage, and slender tibia were detected as factors that might contribute to earlier development of SF. The modeling methodology used in the current study may be helpful in identifying individuals at risk to develop SF.