Domain-independent simulation of physiologically relevant callus shape in mechanoregulated models of fracture healing

Computational models of bone fracture healing and applications: a review

Fracture healing is a very complex physiological process involving multiple events at different temporal and spatial scales, such as cell migration and tissue differentiation, in which mechanical stimuli and biochemical factors assume key roles. With the continuous improvement of computer technology in recent years, computer models have provided excellent solutions for studying the complex process of bone healing. These models not only provide profound insights into the mechanisms of fracture healing, but also have important implications for clinical treatment strategies. In this review, we first provide an overview of research in the field of computational models of fracture healing based on CiteSpace software, followed by a summary of recent advances, and a discussion of the limitations of these models and future directions for improvement. Finally, we provide a systematic summary of the application of computational models of fracture healing in three areas: bone tissue engineering, fixator optimization and clinical treatment strategies. The application of computational models of bone healing in clinical treatment is immature, but an inevitable trend, and as these models become more refined, their role in guiding clinical treatment will become more prominent.

Influence of implant base material on secondary bone healing: an in silico study

The implant material at the fracture site influences fracture healing not only from biological perspective but also from mechanical perspective. Biodegradable implants such as magnesium (Mg) based alloys have shown faster secondary bone healing properties as compared to bioinert implants such as titanium (Ti). The general reasoning behind this is the benefit of Mg from biocompatibility perspectives. We studied the effect of Ti and Mg as base materials for implants from mechanical perspectives, where we focused on the displacements at the fracture site of the tibia and their influence on the stimulus for bone healing. We found out that in comparison to Ti, Mg implants have minimal stress shielding problem, only which led to better mechanical stimulus at the fracture site.

Three-Dimensional Computational Model Simulating the Initial Callus Growth during Fracture Healing in Long Bones: Application to Different Fracture Types

Bone fractures are among the most common and potentially serious injuries to the skeleton, femoral shaft fractures being especially severe. Thanks to recent advances in the area of in silico analysis, several approximations of the bone healing process have been achieved. In this context, the objective of this work was to simulate the initial phase of callus formation in long bones, without a pre-meshed domain in the 3D space. A finite element approach was computationally implemented to obtain the values of the cell concentrations along the whole domain and evaluate the areas where the biological quantities reached the thresholds necessary to trigger callus growth. A voxel model was used to obtain the 3D domain of the bone fragments and callus. A mesh growth algorithm controlled the addition of new elements to the domain at each step of the iterative procedure until complete callus formation. The implemented approach is able to reproduce the generation of the primary callus, which corresponds to the initial phase of fracture healing, independently of the fracture type and complexity, even in the case of several bone fragments. The proposed approach can be applied to the most complex bone fractures such as oblique, severely comminuted or spiral-type fractures, whose simulation remains hardly possible by means of the different existing approaches available to date.

Rethinking the 10% strain rule in fracture healing: A distal femur fracture case series

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.

Image-based radiodensity profilometry measures early remodeling at the bone-callus interface in sheep

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.