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

Schwarzenberg, Peter; Ren, Tianyi; Klein, Karina; Rechenberg, Brigitte von; Darwiche, Salim; Dailey, Hannah L.

doi:10.1016/j.jbiomech.2021.110300

Cited by 8 publications

(12 citation statements)

References 25 publications

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“…As shown in the 6‐week postoperative X‐ray image (Figure 8), evidence of callus formation first begins to emerge in the regions surrounding the fracture gap. Over time, this callus expands into and around the fracture gap, producing a mineralization front that progressively stiffens the construct and reduces the overall strain values 44 . This healing pattern has also been observed in normally healing ovine tibia treated with a medial LCP; both in vivo and in a strain‐based mechanoregulated model 45 .…”

Section: Discussionmentioning

confidence: 57%

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

Inacio

Schwarzenberg

Kantzos

et al. 2022

Journal Orthopaedic Research

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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.

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Section: Discussionmentioning

confidence: 57%

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

Inacio

Schwarzenberg

Kantzos

et al. 2022

Journal Orthopaedic Research

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“…This density value can then be converted to a Young's modulus using a species-specific scaling law. For ovine cortical bone, we recommend the equation derived by (Schwarzenberg et al 2021), which produces an average Young's modulus, 𝐸 𝑖𝑛𝑡𝑎𝑐𝑡 = 12.9 GPa for intact bone. After selecting 𝐸 𝑖𝑛𝑡𝑎𝑐𝑡 and matching 𝑡 and 𝑡 𝑐 to the chosen computational model, the following scaled remodeling function can be used to validate the model predictions:…”

Section: Discussionmentioning

confidence: 99%

“…Recently, we applied a mechanoregulatory model of fracture healing to show that the rate of healing depends on the geometry of the fracture and that all fracture types experience a small healing delay with torsional instability (Ren and Dailey 2020). We also showed that modifying a strain-based mechanoregulatory model of fracture healing to include a geometric proximity function can successfully restrict callus formation to the region near the fracture line and achieve simulation domain independence (Schwarzenberg et al 2021).…”

Section: Introductionmentioning

confidence: 99%

“…The validation strategy used for most recent mechanoregulation models has focused on the global structural mechanics of the limb and qualitative comparison of model predictions to histological analysis of tissue in the callus. For example, the assessment of a model's performance in predicting the spatial and temporal development of tissues in the callus is usually based on only the general trends of mechanical data (e.g., torsional rigidity) (Ren and Dailey 2020;Schwarzenberg et al 2021) or temporal data (e.g., bridging time, interfragmentary motion) (Lacroix and Prendergast 2002;Isaksson et al 2006;Wehner et al 2014;Pietsch et al 2018). Ideally, the localized tissue composition and distribution should also be investigated to assess whether tissue growth and differentiation criteria within the algorithms are functioning correctly.…”

Section: Introductionmentioning

confidence: 99%

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

Ren

Klein

Rechenberg

et al. 2022

Biomech Model Mechanobiol

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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.

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“…This density value can then be converted to a Young's modulus using a species-specific scaling law. For ovine cortical bone, we recommend the equation derived by (Schwarzenberg et al 2021), which produces an average Young's modulus, = 12.9 GPa for intact bone. After selecting and matching and to the chosen computational model, the following scaled remodeling function can be used to validate the model predictions:…”

Section: Discussionmentioning

confidence: 99%

Image-Based Radiodensity Profilometry Measures Early Remodeling at the Bone-Callus Interface in Sheep

Ren¹

2021

Preprint

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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.

show abstract

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

Cited by 8 publications

References 25 publications

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

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

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

Image-Based Radiodensity Profilometry Measures Early Remodeling at the Bone-Callus Interface in Sheep

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