Effects of strain artefacts arising from a pre-defined callus domain in models of bone healing mechanobiology

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.

A review on design of scaffold for osteoinduction: Toward the unification of independent design variables

Biophysical stimulus quantifies the osteoinductivity of the scaffold concerning the mechanoregulatory mathematical models of scaffold-assisted cellular differentiation. Consider a set of independent structural variables ($) that comprises bulk porosity levels ([Formula: see text]) and a set of morphological features of the micro-structure ([Formula: see text]) associated with scaffolds, i.e., [Formula: see text]. The literature suggests that biophysical stimulus ([Formula: see text]) is a function of independent structural variables ($). Limited understanding of the functional correlation between biophysical stimulus and structural features results in the lack of the desired osteoinductivity in a scaffold. Consequently, it limits their broad applicability to assist bone tissue regeneration for treating critical-sized bone fractures. The literature indicates the existence of multi-dimensional independent design variable space as a probable reason for the general lack of osteoinductivity in scaffolds. For instance, known morphological features are the size, shape, orientation, continuity, and connectivity of the porous regions in the scaffold. It implies that the number of independent variables ([Formula: see text]) is more than two, i.e., [Formula: see text], which interact and influence the magnitude of [Formula: see text] in a unified manner. The efficiency of standard engineering design procedures to analyze the correlation between dependent variable ([Formula: see text]) and independent variables ($) in 3D mutually orthogonal Cartesian coordinate system diminishes proportionally with the increase in the number of independent variables ([Formula: see text]) (Deb in Optimization for engineering design-algorithms and examples, PHI Learning Private Limited, New Delhi, 2012). Therefore, there is an immediate need to devise a framework that has the potential to quantify the micro-structural's morphological features in a unified manner to increase the prospects of scaffold-assisted bone tissue regeneration.

Optimal time-dependent levels of weight-bearing for bone fracture healing under Ilizarov circular fixators

It is known that weight-bearing exercises under Ilizarov circular fixators (ICF) could enhance bone fracture healing by mechano-regulation. However, interfragmentary movements at the fracture site induced by weight-bearing may inhibit angiogenesis and ultimately delay the healing process. To tackle this challenge, a computational model is presented in this study which considers the spatial and temporal changes in mechanical properties of fracture callus to predict optimal levels of weight-bearing during fracture healing under ICF. The study takes sheep fractures as example and shows that the developed model has the capability of predicting patient specific, time-dependent optimal levels of weight-bearing which enhances mechano-regulation mediated healing without hindering the angiogenesis process. The results demonstrate that allowable level of weight-bearing and timings depend on fracture gap size. For normal body weights (BW) and moderate fracture gap sizes (e.g. 3 mm), weight-bearing with 30% BW could start by week 4 post-operation and gradually increase to 100% BW by week 11. In contrast, for relatively large fracture gap sizes (i.e. 6 mm), weight-bearing is recommended to commence in later stages of healing (e.g. week 11 post-operation). Furthermore, increasing ICF stiffness (e.g. using half pins instead of pretension wires) can increase the level of weight-bearing significantly in the early stages up to a certain time point (e.g. week 8 post-operation) beyond which no noticeable benefits could be achieved. The findings of this study have potential applications in designing post-operative weight bearing exercises.

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

Mechanoregulatory models have been used to predict the progression of bone fracture healing for more than two decades. However, many published studies share the same fundamental limitation: callus development proceeds within a pre-defined domain that both restricts and directs healing and leads to some non-physiologic healing patterns. To address this limitation, we added two spatial proximity functions to an existing mechanoregulatory model of fracture healing to control the localization of callus within the healing domain. We tested the performance of the new model in an idealized ovine tibial osteotomy with medial plate fixation using three sizes of healing domains and multiple variations of the spatial proximity functions. All model variations produced outward callus growth and bridging weighted toward the far cortex, which is consistent with in vivo healing. With and without the proximity functions, there were marked differences in the predicted callus volume and shape. With no proximity functions, the callus produced was strongly domain dependent, with a 15% difference in volume between the smallest and largest initialization domains. With proximity function control, callus growth was restricted to near the fracture line and there was only 2% difference in volume between domain sizes. Superimposing both proximity functions - one to control outward growth and one representing a decay in periosteal activity away from the fracture - produced a predicted callus size that was within the physiologic range for sheep and had a realistic morphology when compared with fluorescent dye co-localization with calcium deposition over time and histology.

Morphology of bony callus growth in healing of a sheep tibial osteotomy

Long bone fractures typically heal via formation of an external callus, which helps stabilise the bone fragments. Callus composition and morphology influence the mechanical environment, which in turn regulates the progression of healing. Therefore characterising callus development over time is crucial in understanding this mechanobiological regulation. Although bony callus is often assumed to grow towards the fracture from either side, this is not consistent with observations from large animal studies and clinical cases. Therefore, we sought to quantify the morphology of bony callus over time in a large animal model. Sheep tibiae were x-rayed weekly over eight weeks following an osteotomy (n=5), with fixation allowing up to 10% axial displacement under normal weight-bearing. After scaling radiographs by known landmarks and normalising greyscales, bony callus boundaries were defined by manual segmentation. The lateral callus area and coordinates of its centroid were calculated from each image. The external callus initially formed adjacent to the osteotomy site. Over the first four weeks, callus growth from its outer surfaces was characterised by its centre of area moving outwards and away from the osteotomy, on both proximal and distal fragments. Subsequent weeks showed consolidation and resorption from the outer surface of the callus. Our approach allowed bony callus development to be tracked in individuals throughout healing. Contrary to the view that periosteal bone formation originates distant from the fracture, our data showed bony callus adjacent to the defect from early stages, followed by approximately concentric growth. This discrepancy highlights the need for data specific to experimental conditions, and particularly early stages of healing, for evaluating theoretical models of mechanical regulation.

Computational modeling of human bone fracture healing affected by different conditions of initial healing stage

BACKGROUND

Bone healing process includes four phases: inflammatory response, soft callus formation, hard callus development, and remodeling. Mechanobiological models have been used to investigate the role of various mechanical and biological factors on bone healing. However, the effects of initial healing phase, which includes the inflammatory stage, the granulation tissue formation, and the initial callus formation during the first few days post-fracture, are generally neglected in such studies.

METHODS

In this study, we developed a finite-element-based model to simulate different levels of diffusion coefficient for mesenchymal stem cell (MSC) migration, Young's modulus of granulation tissue, callus thickness and interfragmentary gap size to understand the modulatory effects of these initial phase parameters on bone healing.

RESULTS

The results quantified how faster MSC migration, stiffer granulation tissue, thicker callus, and smaller interfragmentary gap enhanced healing to some extent. However, after a certain threshold, a state of saturation was reached for MSC migration rate, granulation tissue stiffness, and callus thickness. Therefore, a parametric study was performed to verify that the callus formed at the initial phase, in agreement with experimental observations, has an ideal range of geometry and material properties to have the most efficient healing time.

CONCLUSIONS

Findings from this paper quantified the effects of the initial healing phase on healing outcome to better understand the biological and mechanobiological mechanisms and their utilization in the design and optimization of treatment strategies. It is also demonstrated through a simulation that for fractures, where bone segments are in close proximity, callus development is not required. This finding is consistent with the concepts of primary and secondary bone healing.

Age-Related Changes in the Mechanical Regulation of Bone Healing Are Explained by Altered Cellular Mechanoresponse

Increasing age is associated with a reduced bone regeneration potential and increased risk of morbidities and mortality. A reduced bone formation response to mechanical loading has been shown with aging, and it remains unknown if the interplay between aging and mechanical stimuli during regeneration is similar to adaptation. We used a combined in vivo/in silico approach to investigate age-related alterations in the mechanical regulation of bone healing and identified the relative impact of altered cellular function on tissue patterns during the regenerative cascade. To modulate the mechanical environment, femoral osteotomies in adult and elderly mice were stabilized using either a rigid or a semirigid external fixator, and the course of healing was evaluated using histomorphometric and micro-CT analyses at 7, 14, and 21 days post-surgery. Computer models were developed to investigate the influence of the local mechanical environment within the callus on tissue formation patterns. The models aimed to identify the key processes at the cellular level that alter the mechanical regulation of healing with aging. Fifteen age-related biological alterations were investigated on two levels (adult and elderly) with a design of experiments setup. We show a reduced response to changes in fixation stability with age, which could be explained by reduced cellular mechanoresponse, simulated as alteration of the ranges of mechanical stimuli driving mesenchymal stem cell differentiation. Cellular mechanoresponse has been so far widely ignored as a therapeutic target in aged patients. Our data hint to mechanotherapeutics as a potential treatment to enhance bone healing in the elderly. © 2019 American Society for Bone and Mineral Research.

Bone fracture healing in mechanobiological modeling: A review of principles and methods

Bone fracture is a very common body injury. The healing process is physiologically complex, involving both biological and mechanical aspects. Following a fracture, cell migration, cell/tissue differentiation, tissue synthesis, and cytokine and growth factor release occur, regulated by the mechanical environment. Over the past decade, bone healing simulation and modeling has been employed to understand its details and mechanisms, to investigate specific clinical questions, and to design healing strategies. The goal of this effort is to review the history and the most recent work in bone healing simulations with an emphasis on both biological and mechanical properties. Therefore, we provide a brief review of the biology of bone fracture repair, followed by an outline of the key growth factors and mechanical factors influencing it. We then compare different methodologies of bone healing simulation, including conceptual modeling (qualitative modeling of bone healing to understand the general mechanisms), biological modeling (considering only the biological factors and processes), and mechanobiological modeling (considering both biological aspects and mechanical environment). Finally we evaluate different components and clinical applications of bone healing simulation such as mechanical stimuli, phases of bone healing, and angiogenesis.