New approach methodologies (NAMs) can reduce reliance on animal testing and enable outcomes assessments in humans that were previously possible only in animal studies. Translating NAMs from animals to clinical use requires consideration of differences between the preclinical and clinical settings. The objective of this study was to translate and assess the performance of virtual mechanical testing of tibial fracture healing from a large animal model to clinical use. We translated a dual-zone material model for soft and hard callus, which we previously validated in sheep, to clinical use. Image-based models, also known as digital twins, were generated from computed tomography (CT) scans of healing human tibiae at 12 weeks post-op. Scaling adjustments were applied to correct for scanner-specific variability in X-ray attenuation values. The threshold for differentiation between soft and hard callus was inferred from sheep using comparative densiometric analysis. The selected hard/soft callus cutoff value was 998 Hounsfield units (HU), corresponding to 0.5372 of the expected cortical bone density mode of 1858 HU. The human-scaled dual-zone model reduced virtual torsional rigidity (VTR) by 41% compared to a single-zone material model developed based on cortical bone mechanics. With the dual-zone model, half the cohort achieved torsional rigidities in the range of intact tibiae, which corresponded well with modified radiographic union score for tibial fractures (mRUST) scores showing that half the patients achieved union (mRUST >= 11) at this timepoint. These results demonstrate the potential for translation of a validated preclinical virtual mechanical test to clinical use.

Torsion is the preferred mode of loading for ex vivo whole-bone mechanical testing due to its robustness to alignment artifacts and ease of implementation. Results from a nondestructive torsion test are usually reported as torsional stiffness, S, or the slope of the torque-angle curve. However, torsional stiffness depends on specimen working length and cannot be compared between experiments with different bone lengths or test setups. Alternatively, the length-independent torsional rigidity can be calculated as GJ = S × L, using the working length L of the specimen. This paper presents evidence that the effective working length exceeds the length of the unpotted bone segment and depends on the amount of twisting allowed by the fixture through the potted ends. Multiple fixture design parameters were systematically varied to quantify how each individual change influenced the effective working length. Common variations in design parameters related to potting contributed up to 5.15% variation in effective working length, while changing the method of coupling the sample to the test frame contributed up to 17.1% variation. These results suggest that effective working length calibration is essential to enable data aggregation between experiments conducted with different setups. To assist other researchers who wish to calibrate their own setups, this investigation also provides practical guidance on how to determine the effective working length of a complex torsion test assembly using finite element analysis with nonlinear contact mechanics. Detailed procedures for setting up a contact solution are documented with recommendations on adjustments to achieve convergence.

In large animal models of bone fracture repair, postmortem torsional testing is commonly used to assess healing biomechanics. Bending and axial tests are physiologically relevant, but much less commonly performed. Virtual torsional testing using image-based finite element models has been validated to postmortem bench tests, but its predictive value for capturing whole-bone mechanics and fracture healing quality under other physiologically relevant loading modes has not yet been established. Accordingly, the purpose of this study was to evaluate the association between mechanical biomarkers derived from virtual torsion, axial, and bending tests under strict alignment and malalignment conditions. Computed tomography (CT) scans from 24 intact and operated sheep tibiae and 29 human tibial fractures were used to create digital twins that were subjected to torsion, axial, and bending tests. The results indicated that torsional rigidity is a strong surrogate for bending flexural rigidity in both ovine and human bones. Torsional rigidity and axial stiffness were strongly correlated in the ovine data, but only moderately in human fractures due to the complex fracture patterns. Axial testing was highly prone to stiffness estimation errors as high as 50% if the applied load and anatomic axis were not perfectly aligned. In contrast, torsional rigidity had errors <1.3% for all malalignment scenarios. Based on this study, virtual torsional rigidity is the recommended summary mechanical biomarker of bone healing because it captures variations in healing biomechanics that are present in other loading modes with a simple setup that is insensitive to alignment error.

Fracture healing is a mechanoregulated process that gradually restores the mechanical integrity of an injured bone. This talk with present a historical perspective on engineering contributions to the modern understanding of mechanoregulation in fracture healing and a current assessment of challenges and opportunities where engineers can contribute to basic and clinical sciences. Starting from the seminal work of Prof. Stephan Perren in the 1970s, half a century of translational research has defined a nuanced connection between the engineering design of fracture fixation implants and healing outcomes. Decades of engineering iterations on external fixators, plates, and intramedullary nails have been tested in large animal models and clinical studies to reveal guiding principles for fracture fixation. These studies collectively explain how mechanical strain generated through interfragmentary motion is both a driver and limiter of the secondary healing response. Yet, challenges persist with clinical translation of new technologies that suggest opportunities for engineers to contribute novel tools for clinical outcomes assessment and device evaluation. Emerging technologies in this space include image-based mechanical biomarkers, wearable technologies, and mobile device data. Beyond implant design, the analytical toolkit of engineering mechanics presents new opportunities to enrich the study of mechanobiology. Virtual mechanical testing can provide spatial insights into the 3D strain environment around a healing fracture – data that cannot be measured any other way. To achieve this, current engineering challenges include real-time data acquisition to monitor activity and the need for improved approaches for image analysis and data mining. Looking to the future, prediction of and early intervention for fracture nonunion remains a major unsolved clinical problem. Addressing this need will require the development of digital twins that combine imaging data, loading data, and next-generation predictive mechanoregulation models to identify and treat nonunions as early as possible.

AimsThe “2 to 10% strain rule” for fracture healing has been widely interpreted to mean that interfragmentary strain greater than 10% predisposes a fracture to nonunion. This interpretation focuses on the gap-closing strain (axial micromotion divided by gap size), ignoring the region around the gap where osteogenesis typically initiates. The aim of this study was to measure gap-closing and 3D interfragmentary strains in plated ovine osteotomies and associate local strain conditions with callus mineralization.MethodsMicroCT scans of eight female sheep with plated mid-shaft tibial osteotomies were used to create image-based finite element models. Virtual mechanical testing was used to compute postoperative gap-closing and 3D continuum strains representing compression (volumetric strain) and shear deformation (distortional strain). Callus mineralization was measured in zones in and around the osteotomy gap.ResultsGap-closing strains averaged 51% (mean) at the far cortex. Peak compressive volumetric strain averaged 32% and only a small tissue volume (average 0.3 cm3) within the gap experienced compressive strains > 10%. Distortional strains were much higher and more widespread, peaking at a mean of 115%, with a mean of 3.3 cm3 of tissue in and around the osteotomy experiencing distortional strains > 10%. Callus mineralization initiated outside the high-strain gap and was significantly lower within the fracture gap compared to around it at nine weeks.ConclusionOvine osteotomies can heal with high gap strains (> 10%) dominated by shear conditions. High gap strain appears to be a transient local limiter of osteogenesis, not a global inhibitor of secondary fracture repair.Cite this article: Bone Joint Res 2025;14(1):5–15.

Virtual mechanical testing with image-based digital twins enables subject-specific insights about the mechanical progression of bone fracture healing directly from imaging data. However, this technique is currently limited by the need for commercial software packages that require manual input to create finite element (FE) models from computed tomography (CT) scans. The purpose of this study was to develop automated image analysis algorithms that can create subject-specific models from CT scans without a human in the loop. Two competing techniques were developed and tested on an imaging dataset consisting of 26 intact and 44 osteotomized ovine tibiae. In both techniques, the raw image was cropped to an efficient bounding box, downsampled, segmented by an element-formation threshold, and cleaned up for efficient FE analysis using voxel-based meshes. The key difference between contour-free (CFT) and snake-reliant (SRT) techniques was threshold- and contour-based segmentation of images, respectively, before bounding box detection. The contours were detected using a snake that balanced desired aspects of the contours through energy minimization. Virtual torsion tests were performed and the results were validated by comparison to ground-truth experimental data. The CFT and SRT models produced nearly identical predictions of virtual torsional rigidity and both methods reliably replicated the physical tests. Models generated by SRT were faster to solve, but model preparation and solution combined was faster by CFT. Automatic digital twin creation by CFT is therefore recommended except where other downstream analyses require systematic spatial data sampling of the bone, which is only achieved by SRT.

Virtual mechanical testing on image-based bone models (digital twins) provides subject-specific insights about the mechanical behavior of a bone during fracture healing. However, the established workflows for these tests are limited by reliance on commercial software and time-consuming manual procedures needed to create the digital twins. To overcome these barriers to clinical adoption and scalability, we have developed methods for user-independent and automated model generation. This study aimed to: (1) compare four competing methods for digital twin creation (two manual versus two automated approaches), (2) assess the influence of model-creation procedures and choice of material model (single- and dual-zone) on the virtual test results, and (3) evaluate the accuracy of the model-creation techniques through experimental validation of the results. Digital twins were generated from 59 CT scans (33 operated osteotomy fractures, 26 contralateral intact bones). Torsional rigidities were compared between modeling workflows and validated using postmortem physical mechanical test data. There were no significant differences in torsional rigidity between any of the four virtual testing groups and physical testing when a dual-zone material model was implemented for bone and callus. These results confirm that virtual mechanical testing is a reliable alternative to physical mechanical testing for assessing intact and healing long bones, with resilience to variations in digital twin creation methods. Automated model creation was substantially faster than the manual approaches, suggesting that automatic digital twin analysis is the pathway toward future clinical scalability.

Despite modern advancements in nailing techniques, delayed healing and nonunion of tibial fractures remains an important clinical problem. Tibial nonunions are reported to occur at a rate of 7–19 % based on data from North American Level 1 trauma centres. Patients may require repeated operations over a protracted period of care. These nonunions finally heal at an average of 20 months after the initial injury. Early evidence from ovine studies and clinical trials has suggested that axial micromotion mediates faster tibial fracture healing compared to rigid fixation. In this case series, we present our experience with treating tibial shaft fracture nonunion with an intramedullary micromotion nail.

The goal of this study was to develop an image analysis algorithm for quantifying the effects of remodelling on cortical bone during early fracture healing. An adaptive thresholding technique with boundary curvature and tortuosity control was developed to automatically identify the endocortical and pericortical boundaries in the presence of high-gradient bone mineral density (BMD) near the healing zone. The algorithm successfully detected boundaries in more than 47,000 microCT images from 12 pairs of healing ovine osteotomies and intact contralateral tibiae. Resampling techniques were used to achieve data dimensionality reduction on the segmented images, allowing characterisation of radial, circumferential, and axial distributions of cortical BMD. Local (transverse slice) and total (whole bone) remodelling scores were produced. These surrogate measures of cortical remodelling derived from BMD revealed that cortical changes were detectable throughout the region covered by callus and that the localised loss of cortical BMD was highest near the osteotomy. Total remodelling score was moderately and significantly correlated with callus volume and mineral composition (r > 0.64, p < 0.05), suggesting that the cortex may be a source of mineral needed to build callus.

As scientific advancements continue to reshape the world, it becomes increasingly crucial to uphold ethical standards and minimize the potentially adverse impact of research activities. In this context, the implementation of the 3R principles-Replacement, Reduction, and Refinement-has emerged as a prominent framework for promoting ethical research practices in the use of animals. This article aims to explore recent advances in integrating the 3R principles into fracture healing research, highlighting their potential to enhance animal welfare, scientific validity, and societal trust. The review focuses on in vitro, in silico, ex vivo, and refined in vivo methods, which have the potential to replace, reduce, and refine animal experiments in musculoskeletal, bone, and fracture healing research. Here, we review material that was presented at the workshop "Implementing 3R Principles into Fracture Healing Research" at the 2023 Orthopedic Research Society (ORS) Annual Meeting in Dallas, Texas.

Bone fracture healing is a complex physiological process influenced by biomechanical and biomolecular factors. Mechanical stability is crucial for successful healing, and disruptions can lead to delayed healing or nonunion. Bone commonly heals itself through secondary fracture healing, which is governed by the mechanical strain at the fracture site. To investigate these phenomena, a validated methodology for capturing the mechanoregulatory process in specimen-specific models of fracture healing could provide insight into the healing process. This study implemented a prognostic healing simulation framework to predict healing trajectories based on mechanical stimuli. Sixteen sheep were subjected to a 3 mm transverse tibial mid-shaft osteotomy, stabilized with a custom plate, and equipped with displacement transducer sensors to measure interfragmentary motion over 8 weeks. Computed tomography scans were used to create specimen-specific bone geometries for finite element analysis. Virtual mechanical testing was performed iteratively to calculate strains in the callus region, which guided tissue differentiation and consequently, healing. The predicted healing outcomes were compared to continuous in vivo sensor data, providing a unique validation data set. Healing times derived from the in vivo sensor and in silico sensor showed no significant differences, suggesting the potential for these predictive models to inform clinical assessments and improve nonunion risk evaluations. This study represents a crucial step towards establishing trustworthy computational models of bone healing and translating these to the preclinical and clinical setting, enhancing our understanding of fracture healing mechanisms. Clinical significance: Prognostic bone fracture healing simulation could assist in non-union diagnosis and prediction.

In large animal studies, the mechanical reintegration of the bone fragments is measured using postmortem physical testing, but these assessments can only be performed once, after sacrifice. Image-based virtual mechanical testing is an attractive alternative because it could be used to monitor healing longitudinally. However, the procedures and software required to perform finite element analysis (FEA) on subject-specific models for virtual mechanical testing can be time consuming and costly. Accordingly, the goal of this study was to determine whether a simpler image-based geometric measure-the torsion constant, sometimes known as polar moment of inertia-can be reliably used as a surrogate measure of bone healing in large animals. To achieve this, postmortem biomechanical testing and microCT scans were analyzed for a total of 33 operated and 20 intact ovine tibiae. An image-processing procedure to compute the attenuation-weighted torsion constant from the microCT scans was developed in MATLAB and this code has been made freely available. Linear regression analysis was performed between the postmortem biomechanical data, the results of virtual mechanical testing using FEA, and the torsion constants measured from the scans. The results showed that virtual mechanical testing is the most reliable surrogate measure of postmortem torsional rigidity, having strong correlations and high absolute agreement. However, when FEA is not practical, the torsion constant is a viable alternative surrogate measure that is moderately correlated with postmortem torsional rigidity and can be readily calculated.

The purpose of this review is to summarize insights gained by finite element (FE) model-based mechanical biomarkers of bone for in vivo assessment of bone development and adaptation, fracture risk, and fracture healing. Muscle-driven FE models have been used to establish correlations between prenatal strains and morphological development. Postnatal ontogenetic studies have identified potential origins of bone fracture risk and quantified the mechanical environment during stereotypical locomotion and in response to increased loading. FE-based virtual mechanical tests have been used to assess fracture healing with higher fidelity than the current clinical standard; here, virtual torsion test data was a better predictor of torsional rigidity than morphometric measures or radiographic scores. Virtual mechanical biomarkers of strength have also been used to deepen the insights from both preclinical and clinical studies with predictions of strength of union at different stages of healing and reliable predictions of time to healing. Image-based FE models allow for noninvasive measurement of mechanical biomarkers in bone and have emerged as powerful tools for translational research on bone. More work to develop nonirradiating imaging techniques and validate models of bone during particularly dynamic phases (e.g., during growth and the callus region during fracture healing) will allow for continued progress in our understanding of how bone responds along the lifespan.

Since the 1970s, the 2%-10% rule has been used to describe the range of interfragmentary gap closure strains that are conducive for secondary bone healing. Interpreting the available evidence for the association between strain and bone healing remains challenging because interfragmentary strain is impossible to directly measure in vivo. The question of how much strain occurs within and around the fracture gap is also difficult to resolve using bench tests with osteotomy models because these do not reflect the complexity of injury patterns seen in the clinic. To account for these challenges, we used finite element modeling to assess the three-dimensional interfragmentary strain in a case series of naturally occurring distal femur fractures treated with lateral plating under load conditions representative of the early postoperative period. Preoperative computed tomography scans were used to construct patient-specific finite element models and plate fixation constructs to match the operative management of each patient. The simulations showed that gap strains were within 2%-10% only for the lowest load application level, 20% static body weight (BW). Moderate loading of 60% static BW and above caused gap strains that far exceeded 10%, but in all cases, strains in the periosteal region external to the fracture line remained low. Comparing these findings with postoperative radiographs suggests that in vivo secondary healing of distal femur fractures may be robust to early gap strains much greater than 10% because formation of new bone is initiated outside the gap where strains are lower, followed by later consolidation within the gap.

Abstract Background: Therapies using electromagnetic field technology show evidence of enhanced bone regeneration at the fracture site, potentially preventing delayed or non-unions. Methods: Combined electric and magnetic field (CEMF) treatment was evaluated in two standardized sheep tibia osteotomy models: a 3 mm non-critical size gap model and a 17 mm critical size defect model augmented with autologous bone grafts, both stabilized with locking compression plates. CEMF treatment was delivered across the fracture gap twice daily for 90 mins, starting 4 days post-operatively (post-OP) until sacrifice (9 or 12 weeks post-OP, respectively). Control groups received no CEMF treatment. Bone healing was evaluated radiographically, morphometrically (micro-CT), biomechanically and histologically. Results: In the 3 mm gap model, the CEMF group (n=6) exhibited higher callus mineral density compared to the Control group (n=6), two-fold higher biomechanical torsional rigidity and a histologically more advanced callus maturity (no statistically significant differences). In the 17 mm graft model, differences between the control (n=6) and CEMF group (n=6) were more pronounced. The CEMF group showed a radiologically more advanced callus, a higher callus volume (p=0.003) and a 2.6x higher biomechanical torsional rigidity (p=0.024), combined with a histologically more advanced callus maturity and healing. Conclusions: This study showed that CEMF therapy notably enhanced bone healing resulting in better new bone structure, callus morphology and superior biomechanical properties. This technology could transform a standard inert orthopedic implant into an active device stimulating bone tissue for accelerated healing and regeneration.

The objective of this study was to use patient-specific finite element modeling to measure the 3D interfragmentary strain environment in clinically realistic fractures. The hypothesis was that in the early post-operative period, the tissues in and around the fracture gap can tolerate a state of strain in excess of 10%, the classical limit proposed in the Perren strain theory. Eight patients (6 males, 2 females; ages 22–95 years) with distal femur fractures (OTA/AO 33-A/B/C) treated in a Level I trauma center were retrospectively identified. All were treated with lateral bridge plating. Preoperative computed tomography scans and post-operative X-rays were used to create the reduced fracture models. Patient-specific materials properties and loading conditions (20%, 60%, and 100% body weight (BW)) were applied following our published method.[1] Elements with von Mises strains >10% are shown in the 100% BW loading condition. For all three loading scenarios, as the bridge span increased, so did the maximum von Mises strain within the strain visualization region. The average gap closing (Perren) strain (mean ± SD) for all patient-specific models at each body weight (20%, 60%, and 100%) was 8.6% ± 3.9%, 25.8% ± 33.9%, and 39.3% ± 33.9%, while the corresponding max von Mises strains were 42.0% ± 29%, 110.7% ± 32.7%, and 168.4% ± 31.9%. Strains in and around the fracture gap stayed in the 2–10% range only for the lowest load application level (20% BW). Moderate loading of 60% BW and above caused gap strains that far exceeded the upper limit of the classical strain rule (<10% strain for bone healing). Since all of the included patients achieved successful unions, these findings suggest that healing of distal femur fractures may be robust to localized strains greater than 10%.

Virtual mechanical testing is a method for measuring bone healing using finite element models built from computed tomography (CT) scans. Previously, we validated a dual-zone material model for ovine fracture callus that differentiates between mineralized woven bone and soft tissue based on radiodensity.1 The objective of this study was to translate the dual-zone material model from sheep to two important clinical scenarios: human tibial fractures in early-stage healing and late-stage nonunions.CT scans for N = 19 tibial shaft fractures were obtained prospectively at 12 weeks post-op. A second group of N = 33 tibial nonunions with CT scans were retrospectively identified. The modeling techniques were based on our published method.2 The dual-zone material model was implemented for humans by performing a cutoff sweep for both the 12-week and nonunion groups. Virtual torsional rigidity (VTR) was calculated as VTR = ML/φ [N-m2/°], where M is the moment reaction, L is the diaphyseal segment length, and φ is the angle of twist.As the soft tissue cutoff was increased, the rigidity of the clinical fractures decreased and soft tissue located within the fracture gaps produced higher strains that are not predicted without the dual zone approach. The structural integrity of the nonunions varied, ranging from very low rigidities in atrophic cases to very high rigidities in highly calcified hypertrophic cases, even with dual-zone material modeling.Human fracture calluses are heterogeneous, comprising of woven bone and interstitial soft tissue. Use of a dual-zone callus material model may be instrumental in identifying delayed unions during early healing when callus formation is minimal and/or predominantly fibrous with little mineralization.ACKNOWLEDGEMENTS:This work was supported by the National Science Foundation (NSF) grant CMMI-1943287.

Objectives: Venous thromboembolism (VTE) is a common nosocomial condition, developing frequently in overweight and obese patients. VTE prophylaxis with weight-based enoxaparin dosing may be more effective than the standard dosing regimen for overweight and obese patients; however, weight-based dosing is not practiced routinely. In this pilot study we sought to evaluate prophylactic anticoagulation regimens used for VTE prevention in overweight and obese patients on the Orthopedic-Medical Trauma (OMT) service to inform the need for modification of dosing practices.Methods: This prospective, observational study evaluated the adequacy of current VTE prophylaxis practice at an academic tertiary center, including overweight and obese patients admitted during 2017-2018 to an OMT comanagement service. It included patients hospitalized for at least 3 days with a body mass index (BMI) of =25 and prescribed enoxaparin. Steady-state antifactor Xa trough and peak levels were monitored after three doses. Frequency of in prophylactic range (0.2-0.44) antifactor Xa levels and VTE events were compared by BMI groups and enoxaparin dosing using the ?(2) test.Results: There were 404 inpatients included: 41.1% were overweight (BMI 25-29), 43.4% were obese (BMI 30-39), and 15.6% were morbidly obese (BMI =40). A total of 351 patients (86.9%) received standard dose enoxaparin 30 mg 2 times per day (BID), and 53 patients received enoxaparin 40 mg BID or more. A number of patients (213; 52.7%) did not achieve prophylactic range antifactor Xa levels. A significantly higher number of patients in the overweight group achieved prophylactic range antifactor Xa compared with obese and morbidly obese groups (58.4% vs 41.7% and 33%, P = 0.002 and 0.0007, respectively). Morbidly obese patients treated with enoxaparin 40 mg BID or higher versus enoxaparin 30 mg BID had fewer VTE events (4% vs 10.8%, P = 0.18).Conclusions: The current practice of VTE enoxaparin prophylaxis may not be adequate for overweight and obese OMT patients. Further guidelines are needed to implement weight-based VTE prophylaxis in overweight and obese hospitalized patients.

Background Therapies using electromagnetic field technology show evidence of enhanced bone regeneration at the fracture site, potentially preventing delayed or nonunions. Methods Combined electric and magnetic field (CEMF) treatment was evaluated in two standardized sheep tibia osteotomy models: a 3-mm non-critical size gap model and a 17-mm critical size defect model augmented with autologous bone grafts, both stabilized with locking compression plates. CEMF treatment was delivered across the fracture gap twice daily for 90 min, starting 4 days postoperatively (post-OP) until sacrifice (9 or 12 weeks post-OP, respectively). Control groups received no CEMF treatment. Bone healing was evaluated radiographically, morphometrically (micro-CT), biomechanically and histologically. Results In the 3-mm gap model, the CEMF group ( n = 6) exhibited higher callus mineral density compared to the Control group ( n = 6), two-fold higher biomechanical torsional rigidity and a histologically more advanced callus maturity (no statistically significant differences). In the 17-mm graft model, differences between the Control ( n = 6) and CEMF group ( n = 6) were more pronounced. The CEMF group showed a radiologically more advanced callus, a higher callus volume ( p = 0.003) and a 2.6 × higher biomechanical torsional rigidity ( p = 0.024), combined with a histologically more advanced callus maturity and healing. Conclusions This study showed that CEMF therapy notably enhanced bone healing resulting in better new bone structure, callus morphology and superior biomechanical properties. This technology could transform a standard inert orthopedic implant into an active device stimulating bone tissue for accelerated healing and regeneration.

Bone healing has been traditionally described as a four-phase process: inflammatory response, soft callus formation, hard callus development, and remodeling. The remodeling phase has been largely neglected in most numerical mechanoregulation models of fracture repair in favor of capturing early healing using a pre-defined callus domain. However, in vivo evidence suggests that remodeling occurs concurrently with repair and causes changes in cortical bone adjacent to callus that are typically neglected in numerical models of bone healing. The objective of this study was to use image processing techniques to quantify this early-stage remodeling in ovine osteotomies. To accomplish this, we developed a numerical method for radiodensity profilometry with optimization-based curve fitting to mathematically model the bone density gradients in the radial direction across the cortical wall and callus. After assessing data from 26 sheep, we defined a dimensionless density fitting function that revealed significant remodeling occurring in the cortical wall adjacent to callus during early healing, a 23% average reduction in density compared to intact. This fitting function is robust for modeling radial density gradients in both intact bone and fracture repair scenarios and can capture a wide variety of the healing responses. The fitting function can also be scaled easily for comparison to numerical model predictions and may be useful for validating future mechanoregulatory models of coupled fracture repair and remodeling.