Abstract

Delayed long bone fracture healing and nonunion continue to be a significant socioeconomic burden. While mechanical stimulation is known to be an important determinant of the bone repair process, understanding how the magnitude, mode, and commencement of interfragmentary strain (IFS) affect fracture healing can guide new therapeutic strategies to prevent delayed healing or nonunion. Mouse models provide a means to investigate the molecular and cellular aspects of fracture repair, yet there is only one commercially available, clinically-relevant, locking intramedullary nail (IMN) currently available for studying long bone fractures in rodents. Having access to alternative IMNs would allow a variety of mechanical environments at the fracture site to be evaluated, and the purpose of this proof-of-concept finite element analysis study is to identify which IMN design parameters have the largest impact on IFS in a murine transverse femoral osteotomy model. Using the dimensions of the clinically relevant IMN as a guide, the nail material, distance between interlocking screws, and clearance between the nail and endosteal surface were varied between simulations. Of these parameters, changing the nail material from stainless steel (SS) to polyetheretherketone (PEEK) had the largest impact on IFS. Reducing the distance between the proximal and distal interlocking screws substantially affected IFS only when nail modulus was low. Therefore, IMNs with low modulus (e.g., PEEK) can be used alongside commercially available SS nails to investigate the effect of initial IFS or stability on fracture healing with respect to different biological conditions of repair in rodents.

Introduction

Bone fractures are the most common musculoskeletal condition requiring medical resources in the United States, with more than 7 million patients undergoing fixation or stabilization of long bone fractures per year as estimated in 2010 [1]. While fracture repair is often uneventful, delayed healing and fracture nonunion remain a significant clinical and socioeconomic burden, with 5–10% of femoral and tibial fractures failing to heal fully. As a result, patients with impaired fracture healing require additional revision surgeries, leading to longer hospitalization stays, rehabilitation periods, increased medical expenses, and, importantly, decreased quality of life [24].

Delayed fracture healing and nonunion can occur as a result of biological or mechanical failure. For instance, obesity, diabetes, advanced age, and smoking status can all increase the risks of delayed bone healing and nonunion by altering a patient's biological potential for regenerating tissue [57]. Likewise, improper levels of interfragmentary strain (IFS) [810], defined as the movement within a fracture gap relative to the initial distance between bone fragments after fixation, can potentially delay fracture repair or lead to nonunion. To overcome these barriers, bone grafting or exogenous growth factors can be applied to improve biological potential [1113], and fixation instrumentation can be utilized to manipulate strain to promote bone growth [1416]. Intramedullary (IM) nailing has become the standard of care for diaphyseal fractures of the tibia and femur because periosteal tissue can be better preserved than when internal plates or external fixators are utilized and early weight-bearing is possible [1719]. Surgeons can control fracture micromotion by selecting the nail material and diameter, and by the changing working distance between the interlocking screws [20]. However, while clinical and preclinical studies have established that mechanical strain is an important determinant of the bone repair process [2123], several factors, including the magnitude, mode, and start of IFS, require additional investigation before IFS can be utilized to promote optimal bone repair.

Given their experimental and temporal advantages over clinical and large animal models, including the availability of genetically modified animals, disease models, and monoclonal antibodies, more rapid fracture healing and breeding cycles, and less complicated husbandry [2428], murine models of diaphyseal fractures are prevalent. Such fractures are commonly stabilized with either IM pins (e.g., Kirchner wire or syringe needle) [23,29], locked plates [30], or external fixation devices [31]. However, IM pins do not provide sufficient rotational stability, and locked plates have not been used to investigate the effects of IFS on fracture healing in rodents. External fixators offer the ability to experimentally manipulate IFS throughout the course of healing [31,32], but these devices do not mimic the locked intramedullary nails (IMNs) frequently used in the clinic. RI System's MouseNail is a clinically relevant murine IMN with locking screws that support secondary bone repair of transverse femoral osteotomies [33,34], but this construct is fixed in regards to nail material, diameter, and working distance between interlocking screws; thereby limiting its utility when investigating how IFS impacts fracture repair.

As an alternative option to iteratively designing and manufacturing murine IMNs for in vivo use, finite element (FE) modeling can be utilized to predict IFS distributions. These simulations can also be used to determine the relative contributions of tension, compression, and shear strain within a fracture or to evaluate the stresses within the fixation devices and surrounding bone. Some FE models have been used to quantify IFS throughout the entire time-course of fracture repair [3538], but these studies examined only one fixation device or did not include fixation devices at all. Other groups have utilized FE models to investigate how novel IMN fixation strategies or distinct fracture geometries impact IFS and stresses within the nails and bone [3942]. However, this approach has not been applied toward designing IMNs to stabilize transverse osteotomies or fractures in mice.

In this parametric FE analysis study, we investigated which design aspects of a locked IMN (distance between interlocking bone screws, clearance between nail and bone, and modulus of the nail) have the largest impact on the initial IFS in transverse femoral osteotomies in mice. In doing so, we hypothesized that the modulus of the nail has a larger impact on IFS than the distance between the proximal and distal interlocking screws when boundary conditions, representing maximum gait forces, compress and bend the fixed long bone. The outcomes from this study can be used to guide future in vivo studies.

Materials and Methods

Creating a Digital Mouse Femur From a Micro-Computed Tomography Scan.

An intact right femur from a healthy 10-week-old male C57Bl/6J mouse was scanned at an isotropic voxel size of 12 μm (70 kVp, 114 μA, 300 ms) using a microcomputed tomography scanner (Scanco μCT 40, Scanco Medical, Basersdorf, Switzerland). The femur was stored in ethanol at 4 °C before use. A hydroxyapatite phantom, provided by the manufacturer, was used to convert attenuation to bone mineral density (mg-HA cm−3). To maintain the trabecular bone architecture in the resulting scan, bone was segmented from the soft tissue using a lower threshold of 300 mg-HA cm−3 after applying a Gaussian noise filter (sigma = 0.2, support = 1). The soft tissue voxels were not included in the FE models. Using Scanco Medical's built-in image processing language, disconnected voxels were removed from the resulting segmented file (aim extension) and a stereolithography surface mesh of the bone was generated. The surface mesh was repaired, smoothed, and simplified, in meshlab (open-source) to reduce the total number of triangulated faces and ease computation [43,44]. Finally, to facilitate digital nail insertion and defect creation, the revised surface mesh was converted to a solid volume file (sat extension) using a matlab script (matlab version R2019b, MathWorks, Natick, MA) [45]. The final bone geometry includes the cortical bone with a coarsened trabecular bone architecture.

Inserting the Locked Intramedullary Nail and Transverse Osteotomy.

The solid volume femur was imported into Ansys SpaceClaim (ansys version 19.0, Ansys, Canonsburg, PA) and centered about the global origin. Initially, a cylinder, with a diameter of 0.82 mm and a length of 9.5 mm, was created to mimic the dimensions of the commercially available murine IMN [46]. In subsequent thinner IMN simulations focused on determining whether the rigid nail being investigated could engender IFS levels similar to those in the compliant nail simulations, the diameter of the nail was reduced to 0.74 mm, 0.66 mm, 0.63 mm, and 0.62 mm. In all simulations, two smooth cylinders, with a diameter of 0.33 mm and a length of 4 mm, were placed 1.75 mm or 3.5 mm from the midline of the IMN to represent medial-lateral interlocking screws spaced 3.5 mm and 7 mm apart, respectively. The IMN assembly was centered, visually, within the medullary cavity, and was inserted into the femur using SpaceClaim's built-in Boolean operations. Radial reaming of the bone was performed to create clearance between the nail and bone surfaces equal to 0.005 mm, 0.02 mm, 0.06 mm, or 0.1 mm. For the smaller-diameter rigid nails, the clearance between the nail and bone surfaces was maintained at 0.1 mm. A transverse osteotomy was created by slicing a 0.25 mm layer of bone, centered about the middle of the IMN and midpoint of the diaphysis (Fig. 1(a)). This slice represented a layer of granulation tissue, between the bone cortices, during the initial stage of healing. All disconnected bone fragments were removed from the final assembly.

Fig. 1
(a) A three-dimensional reconstruction of a 0.25 mm osteotomy fixed with an IMN with 7 mm interlocking screw spacing used to quantify the mechanical environments within the granulation tissue region, the nail, and the surrounding bone. Representative images of the octahedral shear strain throughout the (b) entire geometry and (c) granulation tissue layer. (d) Octahedral shear strain within the granulation tissue (median ± IQR) generally increased with increasing nail-bone clearance but the effect of interlocking screw spacing was less consistent in the SS nail simulations.
Fig. 1
(a) A three-dimensional reconstruction of a 0.25 mm osteotomy fixed with an IMN with 7 mm interlocking screw spacing used to quantify the mechanical environments within the granulation tissue region, the nail, and the surrounding bone. Representative images of the octahedral shear strain throughout the (b) entire geometry and (c) granulation tissue layer. (d) Octahedral shear strain within the granulation tissue (median ± IQR) generally increased with increasing nail-bone clearance but the effect of interlocking screw spacing was less consistent in the SS nail simulations.
Close modal

Assigning Material Properties.

The IMN assembly was loaded into the ansys Static Structural module, where the assembly meshed, material properties were assigned, boundary conditions were applied, and simulations were run. The fibrous tissue, IMN, and interlocking screws were meshed using a hexahedral dominant method while the distal and proximal bone fragments were meshed using a patch-independent tetrahedral method. The resulting mesh, with approximately 4.1 × 105 elements and 8.4 × 105 nodes, had an average characteristic length and element quality of 43 μm and 0.73 μm, respectively. As listed in Table 1, each solid body was assigned a Young's modulus (Es) and a Poisson's ratio (ν) value. To predict how IMN stiffness affected IFS, the IMN was designated as either polyetheretherketone (PEEK) or stainless steel (SS). For computational simplicity, all of the materials were considered to be homogeneous, isotropic, and linearly elastic [4749].

Table 1

Mechanical properties of the fixed femur

MaterialEs (MPa)ν
Bone [49]15,0000.30
Granulation Tissue [95]0.20.167
SS [96]193,0000.31
PEEK [96]3,6000.38
MaterialEs (MPa)ν
Bone [49]15,0000.30
Granulation Tissue [95]0.20.167
SS [96]193,0000.31
PEEK [96]3,6000.38

Applying Boundary Conditions and Executing Simulations.

The contact regions between the nail and interlocking screws, between the nail and bone, and between the nail and granulation tissue were defined as frictional (μ = 0.2) [50,51], while the contact regions between the bone and interlocking screws and between the bone and granulation tissue were bonded. To generate a maximum axial gait force of 6 times body weight (BW = 23 g) and a maximum bending moment of 10.7 × BW mm at the mid-diaphysis [5255], a force vector of 0.352 N, 0.11 N, 1.356 N (lateral, anterior, distal) was applied to the surface of the femoral head and the center of the distal femur surface was fixed in all three dimensions (Fig. 1(a)). The analyses were run using the Ansys Mechanical direct solver. Equivalent (von Mises), maximum principal, minimum principal, and maximum shear strains were evaluated for the granulation tissue region while equivalent stress was evaluated for the IMN and distal bone. The values of these invariants of the stress tensor were calculated using built-in evaluation options. Octahedral shear strain (γoct) correlated well with tissue type during fracture healing in rats [56], and so we calculated octahedral shear strain from equivalent strain (εvm) using the following equation [57]
γoct=23εvm
(1)
Medial-lateral (ML), anterior-posterior (AP), and axial displacements were also evaluated to assess fracture motion in the osteotomy using built-in evaluation options (Eq. (2)). The median displacement (s̃) of the distal osteotomy surface nodes was subtracted from the median displacement of the proximal osteotomy surface nodes, and the initial length in all three dimensions was defined as the initial gap size (0.25 mm). A negative axial IFS represents compression, a negative medial-lateral IFS represents the proximal osteotomy surface translating further laterally than the distal osteotomy surface, and a negative anterior-posterior IFS represents the proximal osteotomy surface moving further posteriorly than the distal osteotomy surface. The total magnitude of IFS (combined IFS) was calculated using Eq. (3)
IFSdirectional=100*(s̃proximals̃distal)0.25
(2)
IFScombined=100*s̃proximal,ML2+s̃proximal,AP2+s̃proximal,axial2s̃distal,ML2+s̃distal,AP2+s̃distall,axial20.25
(3)

Finally, to better understand the strain versus clearance trends, the final gap distances between the IMN and endosteal surface of the medullary canal were tabulated using the built-in contact tool option. The gap or distance between a bone element and an adjacent IMN element for the prescribed boundary conditions was recorded for each contact pair around the circumference of the nail. This was done along the length of the IMN (Z-location from −3.5 mm to 6 mm) at increments of 0.25 mm. The percent of IMN circumferential nodes in direct contact with the surrounding bone (gap size = 0 mm) was calculated for each increment and plotted as a function of IMN length (proximal to distal end).

Results

Octahedral Shear Strain in the Fracture Gap Increases With Reduced Nail Modulus and Increased Nail-Bone Clearance.

For all of the simulations, the applied loading vector caused the proximal half of the femur to move primarily in the lateral direction, while the distal half of the femur was nearly motionless due to the fixation point on the distal surface (PEEK nail simulation shown in Fig. 1(b)). Depending on the nail-bone clearance (i.e., reaming diameter) and interlocking screw distance, switching from SS (high modulus) to PEEK (low modulus) resulted in a 1.74–4.07 fold change in median octahedral shear strain within the granulation tissue (Fig. 1(d)). The largest median octahedral shear strain within the granulation tissue was 24.7%, which occurred using a PEEK nail with 7.0 mm interlocking screw spacing and 0.1 mm nail-bone clearance. In contrast, the median octahedral shear strain within the granulation tissue for the SS IMN did not exceed 8.7%, which occurred with 7.0 mm interlocking screw spacing and 0.06 mm nail-bone clearance.

Octahedral shear strain generally increased with increasing clearance between the nail and bone, but this strain versus clearance trend plateaued at smaller clearances in the SS IMN (between 0.02 mm and 0.06 mm) than in the PEEK IMN (between 0.06 mm and 0.1 mm). Switching the interlocking screw spacing from 3.5 mm to 7 mm resulted in 1.17–2.00 and 1.09–2.49 fold changes in median octahedral shear strain within the granulation tissue for the PEEK and SS IMN simulations, respectively. However, the maximum absolute differences in octahedral shear strain between these two interlocking screw spacings were 12.3% and 4.0% for the PEEK and SS IMN simulations, respectively. Furthermore, while this absolute difference in octahedral shear strain widened with increasing clearance between bone and PEEK nail, the absolute difference in octahedral shear strain between 3.5 mm and 7.0 mm interlocking screw spacing is less than 0.5% at both 0.0 mm and 0.1 mm SS IMN-bone clearance (Fig. 1(d))

Shear is the Primary Mode of Strain in the Fracture Gap.

Evaluating the individual strain components revealed that the maximum shear strain was larger than both the maximum principal strain and the absolute value of the minimum principal strain for all fixation strategies (Fig. 2). The absolute value of the minimum principal strain (i.e., compressive strain) exceeded the maximum principal strain (i.e., tensile strain) for the PEEK IMN simulations, but this trend in magnitude was less defined for the SS IMN simulations. Shear being the dominant mode of deformation within the granulation tissue can be explained by IFS typically being larger in the anterior-posterior and medial-lateral direction than in the axial direction (Figs. 3(a)3(d)). IFS generally increased in all three orthogonal directions with increasing clearance between the nail and bone, but, similar to the octahedral shear strain trend, IFS plateaued at smaller clearances in the SS IMNs than in the PEEK IMNs. These data indicate that bending of the IMN is limited for the prescribed boundary conditions with there being less bending in the stiffer SS IMN.

Fig. 2
Maximum shear strain (median±IQR) was the primary mode of strain within the granulation tissue when the osteotomy was fixed with (a) a PEEK IMN with 3.5 mm interlocking screw spacing, (b) a PEEK IMN with 7 mm interlocking screw spacing, (c) a SS IMN with 3.5 mm screw spacing, or (d) a SS IMN with 7 mm interlocking screw spacing
Fig. 2
Maximum shear strain (median±IQR) was the primary mode of strain within the granulation tissue when the osteotomy was fixed with (a) a PEEK IMN with 3.5 mm interlocking screw spacing, (b) a PEEK IMN with 7 mm interlocking screw spacing, (c) a SS IMN with 3.5 mm screw spacing, or (d) a SS IMN with 7 mm interlocking screw spacing
Close modal
Fig. 3
IFS was typically greater in the anterior-posterior and medial-lateral directions than in the proximal-distal direction. (a) Fracture motion was in the posterior direction and in the anterior direction when the nail was SS and PEEK, respectively. One exception was the SS IMN with a spacing of 7 mm between screws and a clearance of 0.1 mm in that the motion of proximal surface switched to the anterior direction. (b) Regardless of spacing and material modulus, fracture motion was in the lateral direction such that medial-lateral IFS was higher for SS than for PEEK IMN. (c) SS IMN caused tensile IFS, while PEEK IMN caused compressive IFS. These strains were less than absolute 5%, except when there was a clearance of 0.1 mm between PEEK IMN and bone (7 mm spacing). (d) The change in the overall magnitude of IFS as clearance increased was similar to the change in octahedral shear strain of the granulation tissue.
Fig. 3
IFS was typically greater in the anterior-posterior and medial-lateral directions than in the proximal-distal direction. (a) Fracture motion was in the posterior direction and in the anterior direction when the nail was SS and PEEK, respectively. One exception was the SS IMN with a spacing of 7 mm between screws and a clearance of 0.1 mm in that the motion of proximal surface switched to the anterior direction. (b) Regardless of spacing and material modulus, fracture motion was in the lateral direction such that medial-lateral IFS was higher for SS than for PEEK IMN. (c) SS IMN caused tensile IFS, while PEEK IMN caused compressive IFS. These strains were less than absolute 5%, except when there was a clearance of 0.1 mm between PEEK IMN and bone (7 mm spacing). (d) The change in the overall magnitude of IFS as clearance increased was similar to the change in octahedral shear strain of the granulation tissue.
Close modal

Stresses in the Nail and Bone Are Primarily Below Yield and Endurance Strengths.

To anticipate whether any of the fixation constructs are likely to fail, equivalent (von Mises) stress was calculated for the IMNs and surrounding bone, and a factor of safety of 2.0 was applied to all relevant yield strengths (Table 2). The highest nail stresses were concentrated at the ends of the IMN and at the interlocking screws (Figs. S1(a)–S1(d) and Fig. S2 available in the Supplemental Materials on the ASME Digital Collection), with fewer than 10% of nodes in the SS IMN predicted to exhibit equivalent stresses above the defined safety threshold for SS (Fig. S1(e) available in the Supplemental Materials). In contrast, fewer than 0.04% of nodes in the PEEK nails were predicted to be exposed to equivalent stresses exceeding the designated threshold for PEEK (Fig. S1(f) available in the Supplemental Materials). For most of the nail-bone clearances investigated, the nails with 7 mm interlocking screw spacing were predicted to contain more regions of high stress than the IMNs with 3.5 mm interlocking screw spacing. While the number of high-stress nodes decreased with increasing nail-bone clearance for the SS IMN with 7 mm interlocking screw spacing, the number of high-stress nodes for the SS nail with 3.5 mm interlocking screw spacing was projected to increase with increasing nail-bone clearance before reaching a maximum at a nail-bone clearance of 0.02 mm and decreasing rapidly with increasing nail-bone clearance. In contrast, the number of high-stress nodes in the PEEK IMNs increased with increasing clearance.

Table 2

Yield and safety threshold stresses of the fixed femur

MaterialYield stress (MPa)Safety threshold (MPa)
Bone [97,98]13065
SS [99]200100
PEEK [99]7035
MaterialYield stress (MPa)Safety threshold (MPa)
Bone [97,98]13065
SS [99]200100
PEEK [99]7035

The equivalent stress within the surrounding bone was evaluated to identify regions of high stress where damage could potentially accumulate. Representative images of the equivalent stress in the bone (Fig. S3(a)–S3(b) available in the Supplemental Materials on the ASME Digital Collection) showed that the regions of higher stress are located in the distal femur. The equivalent stress in the bone surrounding the PEEK IMN was lower than that in the bone surrounding SS IMN, and all of the nodes experiencing high levels of stress were located in the distal end of the bone-IMN assembly. The calculated equivalent stress values exceeded the safety threshold of bone in fewer than 0.25% and 4.5% of distal bone nodes in the PEEK and SS IMN simulations, respectively (Fig. S3(c)–S3(d) available in the Supplemental Materials). In the SS IMN simulations, the percent of high-stress nodes generally decreased with increasing nail-bone clearance, and the bone surrounding the nail with the 7 mm interlocking screw spacing was exposed to higher stresses than that surrounding the nail with the 3.5 mm interlocking screw spacing. In contrast, the percent of high-stress nodes in the bone surrounding the PEEK IMN remained relatively low for all nail-bone clearances investigated. In all of the simulations, the majority of nodes that were subjected to high levels of equivalent stress were concentrated at the interlocking screw, at the bottom of the nail, and at the fixation point (Fig. S4 available in the Supplemental Materials).

Thinner SS IMNs With 7.0 mm Interlocking Screw Spacing Can Provide Higher Levels of IFS While IFS Remains Unchanged for Nails With 3.5 mm Interlocking Screw Spacing.

The initial set of FE models predicted that the octahedral shear strains maintained by the commercially available SS IMN would not exceed 8.7% within the osteotomy and would be similar between the 3.5 mm and 7 mm interlocking screw spacing options when the reaming-nail distance (i.e., gap size) is 0.0 mm or 0.1 mm (Fig. 1(d)). To determine whether it would be possible for rigid SS IMNs to produce levels of IFS comparable to those produced by the compliant PEEK IMNs, the diameter and, therefore, stiffness of the original SS IMN was reduced while maintaining a nail-bone clearance of 0.1 mm. The thinner SS IMN simulations with 3.5 mm interlocking screw spacing predicted a median octahedral shear strain within the osteotomy around 6.3% for all diameters investigated. In the thinner SS IMN simulations with 7.0 mm screw spacing, once the nail diameter was reduced below 0.74 mm, the median octahedral shear strain in the osteotomy increased with decreasing nail size until it reached a maximum value of 10.5% for a 0.62 mm diameter SS IMN (Fig. 4(a)). Similar to the original diameter IMN simulations, shear was the prevailing mode of strain (data not shown).

Fig. 4
(a) The octahedral shear strain within the granulation tissue (median±IQR) only increased with decreasing SS IMN diameter when the interlocking screw spacing is set to 7 mm. (b) The percent of nodes in the thinner SS IMN exceeding the defined safety threshold of SS (100 MPa) decreased with increasing nail diameter but remained relatively low compared to the majority of the original thickness SS IMN simulations (Fig. S1(e) available in the Supplemental Materials on the ASME Digital Collection). (c) The percent of nodes in the distal bone, surrounding the thinner SS IMN, exceeding the defined safety threshold of bone (65 MPa) generally increased with increasing nail diameter but remained relatively low compared to the majority of the original thickness SS IMN simulations (Fig. S3(d) available in the Supplemental Materials).
Fig. 4
(a) The octahedral shear strain within the granulation tissue (median±IQR) only increased with decreasing SS IMN diameter when the interlocking screw spacing is set to 7 mm. (b) The percent of nodes in the thinner SS IMN exceeding the defined safety threshold of SS (100 MPa) decreased with increasing nail diameter but remained relatively low compared to the majority of the original thickness SS IMN simulations (Fig. S1(e) available in the Supplemental Materials on the ASME Digital Collection). (c) The percent of nodes in the distal bone, surrounding the thinner SS IMN, exceeding the defined safety threshold of bone (65 MPa) generally increased with increasing nail diameter but remained relatively low compared to the majority of the original thickness SS IMN simulations (Fig. S3(d) available in the Supplemental Materials).
Close modal

Fewer than 0.3% of nodes in the thinner SS IMNs were predicted to be exposed to equivalent stresses greater than the defined safety threshold of SS; and, for all nail diameters, more nodes in the 7 mm interlocking screw spacing models experienced these high stresses than in the 3.5 mm interlocking screw spacing models (Fig. 4(b)). As the diameter of the SS nail decreased, the percent of nodes in the IMN that exceed the safety threshold was predicted to increase (Fig. 4(b)). In contrast, the surrounding bone generally contained fewer high-stress nodes with decreasing IMN thickness (Fig. 4(c)). The thinner SS IMNs with 7 mm interlocking screw spacing generated more regions of high-stress in the distal bone than those with 3.5 mm screw spacing, but fewer than 0.25% of nodes in the bone were exposed to equivalent stresses greater than the safety threshold. Analogous to the original SS IMN simulations, higher stresses were concentrated near the interlocking screws, the ends of the nail, and the distal bone fixation site (Fig. S5 available in the Supplemental Materials).

Discussion

Clinically relevant murine models can be beneficial for investigating the interplay between fracture biology and biomechanics, because such models can investigate how healing capacity (biology) and mechanical stimulation (rigidity of fixation) work in concert during fracture repair. However, there is currently only one locking IMN construct commercially available for use in mice [33], thereby restricting the capability for modulating the mechanical environment to variable osteotomy size or fracture gap [51]. The purpose of this study was to use a simplified FE model to evaluate the effects of the nail material, interlocking screw spacing, and nail-bone clearance on IFS early in the fracture repair process. Together, these results can be utilized to identify which parameters should be considered when selecting alternative IMN constructs for future in vivo studies. This study demonstrated that switching the IMN material from SS to PEEK consistently resulted in a large increase in IFS (i.e., octahedral strain within the osteotomy or fracture motion per gap size). In contrast, changing interlocking screw spacing had a limited impact on IFS when the osteotomy was fixed with a rigid SS nail. Unless a smaller diameter, the rigid nail can be manufactured and shown to survive normal loading conditions, using nails with variable modulus (rigid to compliant) provides the greatest manipulation of IFS when compared to other parameters (spacing of interlocking screws and reaming clearance).

Interestingly, while an increase in the clearance between the IMN and endosteal bone surface also increased IFS, the increase in IFS plateaued with the stiffer IMN and so reduced the range in IFS that could be achieved by reaming compared to the compliant PEEK nail. The plateauing observed in the stiffer nail is potentially caused by the IM nail no longer making contact with the surrounding bone after loading (Fig. S6 available in the Supplemental Materials on the ASME Digital Collection). The SS nail with 3.5 mm interlocking screw spacing lost contact with the mid-diaphysis between 0.005 mm and 0.02 mm clearance while the SS nail with 7 mm interlocking screw spacing and the PEEK nail with 3.5 mm interlocking screw spacing both lost contact with the mid-diaphysis between 0.06 mm and 0.1 mm clearance. The PEEK nail with 7 mm interlocking screw spacing remained in contact with the mid-diaphysis, irrespective of the initial, before loading clearance.

Intramedullary nails have been utilized clinically for decades to fix long bone fractures. While conventional IMNs are typically fabricated from SS or titanium-based alloys, more compliant PEEK-based nails have begun to show some clinical success in permitting early weight-bearing and promoting accelerated fracture healing [5860]. The simulations herein predicted that a 0.82 mm diameter IMN, fabricated from SS, can produce median octahedral shear strains between 1.4% and 8.7% within a 0.25 mm osteotomy in a murine femur. These strains will likely engender a similar secondary fracture repair response to that observed in vivo with the commercially available SS nail [33]. However, while strains below 2% and 10% are thought to promote primary fracture repair and secondary fracture repair, respectively, in humans with minimal vascular injury [61,62], both bone and cartilage can potentially withstand strains up to 30% in murine fracture models [48,53]. As predicted by the FE models, a PEEK nail with 7.0 mm interlocking screw spacing can be used to access the upper portion of this strain range while a SS nail can be used to engender median octahedral shear strains less than 10% within the osteotomy. Therefore, having access to both a rigid (e.g., SS) and compliant (e.g., PEEK) IMN with 7.0 mm interlocking screw spacing for use in a murine femoral fracture model would facilitate clinically relevant studies investigating the role of the mechanical environment in fracture healing.

To determine whether other SS IMN design parameters can be modified to provide similar levels of IFS to those produced by the PEEK nails, we wanted to investigate the impact of reducing the stiffness of SS nail. Considering that bending stiffness is proportional to diameter of the IMN [20,63], the diameter of the SS nail was systematically reduced to 0.62 mm while maintaining a constant nail-bone clearance. The thinner SS nail simulations predicted that reducing the diameter of the nail has minimal impact on the mechanical environment supported by the SS nail with 3.5 mm interlocking screw spacing while IFS increases with decreasing nail diameter for the SS nail with 7.0 mm interlocking screw spacing once the diameter falls below 0.74 mm. Furthermore, a median octahedral shear strain greater than 10% within the osteotomy can be produced by SS nails with diameters less than or equal to 0.63 mm. However, it is unknown whether a smaller diameter SS IMN can be manufactured and whether it will withstand in vivo cyclic loading without yielding or failing. Moreover, the IFS engendered by using the thinner SS IMN remain well below those generated by the PEEK nail with 7.0 mm interlocking screw spacing. Therefore, a PEEK nail with 7.0 mm interlocking screw spacing will be more effective than a thinner SS nail at providing a high strain environment within a transverse osteotomy.

The FE models in this study also predicted that for the loading condition investigated, shear strain would exceed compressive and tensile strain for all of the nails investigated and that IFS would generally increase with increasing nail-bone clearance. These results are in agreement with other ex vivo and in silico studies that reported shear to be the primary mode of motion supplied by IMNs [64,65], and that increasing the diameter of the IMN or minimizing the annular gap between the nail and endosteal surface reduces interfragmentary motion [51,64]. While some studies have demonstrated that shear strain hinders fracture healing [66,67], others have concluded that shear strain may not be detrimental [68,69]. These conflicting conclusions are likely due in part to IMNs supporting both shear and axial strain [36]. Shear strain was the dominant mode of strain in our simulations, but compressive and tensile strains also existed within the granulation tissue region. The effects of these strain modes and the timing of their application must be investigated further to optimize healing in patients with compromised biological potential

While IMNs can fatigue and break in patients experiencing delayed healing or nonunion [70], immediate failure of the nail was not predicted in any of the simulated IMN constructs examined in this study. For almost all of the nail-bone clearances investigated, the largest percent of nodes supporting high stresses were observed in the original SS IMN construct. While this study only examines the mechanical environment shortly after creating the osteotomy, RI System's SS MouseNail, from which the original SS nail is designed, has demonstrated the ability to maintain fixation over 10 weeks, even in the case of nonunion [34]. While it is currently unknown whether the higher octahedral shear strains predicted for the osteotomies fixed with the PEEK and thinner SS IMNs can potentially alter fracture healing in vivo, the prediction that they will have smaller regions of high stress in the nails and in the surrounding bone suggest that these fixation strategies are less likely than the original SS nail to fail. These results are in agreement with prior clinical reports suggesting that clinically available PEEK nails can share more of the mechanical load with the fracture callus and surrounding bone than SS nails and are, therefore, less likely to fail [71,72].

While these FE simulations contend that a PEEK-based IMN or a smaller diameter SS nail can potentially be used in a clinically relevant murine model for investigating the effects of increased IFS on fracture repair, this study has a number of limitations. To allow movement between the nail and interlocking screws [73], a coefficient of friction of 0.2 was applied. This coefficient of friction has been used in similar FE studies [50,51], but it is unclear whether the amount of micromotion between the two bodies calculated in the simulations will match what will be seen in vivo. Furthermore, even though the loading conditions used in these simulations have been used in previous studies [53,54], it is not currently known whether these forces accurately recapitulate the gait forces observed early in the fracture healing process. To investigate whether the strain versus nail-bone clearance trend (Fig. 1(d)) and the strain mode differences (Fig. 2(b)) observed in this study were dependent on the selected boundary conditions (Fig. 1(a)), the PEEK nail with 3.5 and 7 mm interlocking screw spacing simulations were reanalyzed to include both a hip-joint reaction force and an abductor muscle force (Fig. S9(a) available in the Supplemental Materials) instead of the sole hip-joint reaction force that caused an axial gait force of 6 × BW and a bending moment of 10.7 × BW at the mid-diaphysis in the original simulations (Fig. 1(a)). Due to insufficient information about abductor forces in mice, we adopted the two force vectors from FE models of the human femur in singled-leg stance [7478], but scaled by mouse body weight. In agreement with the original simulations, all the strain modes investigated increased with increasing nail-bone clearance (Figs. S9(d)–S9(f) available in the Supplemental Materials). Even though the inclusion of an abductor force decreased IFS in these simulations (Figs. S9(b)–S9(c) available in the Supplemental Materials) relative to the original simulations (Figs. 1(b)1(c)), maximum shear strain continued to exceed the maximum and minimum principal strains (Figs. 1(e)1(f)).

Another limitation in the parametric study was the fixation of both the medial and lateral condyles (Fig. 1(a)). In FE models of human femurs with an IMN subject to single-leg stance during a gait cycle, a point in the medial condyle was fixed in the three orthogonal directions, thereby allowing rotation of the distal end in the coronal plane and sagittal plane [42,79,80]. By preventing movement of both condyles, the present FE model favored higher stresses in the distal bone than these previous studies. Building the FE model from a scan of a single mouse femur also limits the generalizability of the observed trends, and we predict that IFS values would likely increase as the femur elongates with age. Finally, while mesh convergence testing was performed on the granulation tissue region (Fig. 7 available in the Supplemental Materials on the ASME Digital Collection), the FE models herein were not validated with ex vivo mechanical testing. Consequently, the calculated IFS values may be imprecise. However, we conducted an intact bone simulation, using the same loading vector and fixation point, and calculated median maximum and minimum principal strains of 58 microstrain and 126 microstrain, respectively, along the external surface of the mid-diaphysis of the femur (Fig. 7 available in the Supplemental Materials). These strains are comparable to other in silico studies that have quantified mid-diaphyseal strains in murine tibiae during gait [81,82]. While confirming IFS accuracy will require model validation [83], relative comparisons can still be made between the different fixation groups.

An additional limitation of this study is that clearance between the nail and bone was created by digital reaming. While this process maintained the diameter and, therefore, stiffness of the nail, orthopedic reaming is often coupled with larger nail implantation to increase contact between the IMN and cortical bone and to improve the stiffness of the entire construct [20]. Reaming can also damage the endosteal blood supply [61,84], but studies have shown that the blood supply from the periosteum and surrounding soft tissue can compensate for this loss. While minimal reaming is required for MouseNail implantation [34] and 0.5–1.5 mm over-reaming is appropriate for IMN implantation in humans [85], it is currently unknown whether nail-bone interference will make it more difficult to implant the compliant PEEK IMN and whether additional reaming will be required.

A further limitation is that the FE model geometry of a transverse osteotomy only includes a layer of granulation tissue between the bone cortices rather than a mature callus. This substitution was performed to simplify the simulations, and including more granulation tissue to the model is not expected to significantly affect the IFS trends due to the tissue's relatively low elastic modulus. However, while transverse osteotomies are more consistent regarding size and location than closed fractures created by three-point bending, the creation of these defects induces soft tissue trauma and inflammation. Furthermore, while transverse osteotomies commonly occur in surgical practice, they do not completely mimic traumatic fractures [86].

Finally, while other in silico studies have included other contributing variables, including hydrostatic stress, fluid flow, cellular infiltration, vascularization, oxygen concentration, and growth factors [3538,8790], this study only focusses on identifying how IMN design parameters affect IFS early in the fracture healing process. While all of these variables likely influence fracture repair, deformation has been shown to have a larger impact than hydrostatic pressure of fluid flow on initial healing patterns in sheep [91], and octahedral shear strain correlated well with tissue type during fracture healing in rats [56]. Nonetheless, the simulations herein can be used to identify relative IFS trends, but they cannot be used to predict healing patterns. The transient nature of fracture repair must also be considered when proposing new therapeutic strategies because the mechanical environment can promote or hinder healing at any stage of the healing process [9294]. Despite these limitations, the FE models indicate that PEEK IMNs or thinner SS nails can be used to support levels of IFS greater than what is provided by the commercially available SS IMN.

Conclusions

This proof-of-concept FE modeling study investigated which locking IMN design components have the largest impact on the initial IFS in a murine transverse femur osteotomy model. The FE simulations revealed that IFS generally increases with increasing nail-bone clearance and with decreasing nail modulus. In contrast, while IFS is predicted to increase with increasing interlocking screw spacing for the PEEK IMNs and for SS IMNs with diameters less than 0.74 mm, interlocking screw spacing is projected to have less of an impact on IFS when the original-diameter SS IMN is used. These findings suggest that a compliant PEEK IMN with 7.0 mm interlocking screw spacing can be used alongside a commercially available SS IMN in future in vivo studies to investigate how biological mechanisms and mechanical stimuli affect fracture healing and nonunion in mice.

Acknowledgment

Luis Vega and Chris Power, from OrthoPediatrics, purchased a MouseNail system and provided feedback on the feasibility of changing design parameters. Ansys was accessed through the Vanderbilt University School of Engineering.

Funding Data

  • Biomedical Laboratory Research and Development, VA Office of Research and Development (Grant No. BX005062; Funder ID: 10.13039/100007496).

  • Congressionally Directed Medical Research Programs (Grant No. W81XWH-16-2-0052; Funder ID: 10.13039/100000090).

  • National Center for Research Resources (Grant No. S10RR02763; Funder ID: 10.13039/100000097).

Conflicts of Interest

The authors do not have conflicts of interest to declare.

Nomenclature

Es =

Young's modulus

FE =

finite element

IFS =

interfragmentary strain

IMN =

intramedullary nail

PEEK =

polyetheretherketone

s̃ =

median displacement

SS =

stainless steel

ν =

Poisson's ratio

μ =

coefficient of friction

γoct =

octahedral shear strain

εvm =

equivalent (von Mises) strain

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